BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthias Röger (Technische Universität Dortmund) DTSTART:20200421T150000Z DTEND:20200421T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/1 DESCRIPTION:Title: An obstacle type problem as a limit of a model for cell polarization\nby Matthias Röger (Technische Universität Dortmund) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Goldman (Laboratoire Jacques-Louis Lions and Université P aris 7) DTSTART:20200428T150000Z DTEND:20200428T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/2 DESCRIPTION:Title: On an old conjecture of Almgren\nby Michael Goldman (Laboratoire Ja cques-Louis Lions and Université Paris 7) as part of Lisbon webinar in an alysis and differential equations\n\n\nAbstract\nIn this talk I will give an overview on the few results available on the conjecture of Almgren rega rding the convexity of drops subject to the action of an external potentia l. In particular I will present recent progress in this direction obtained with G. De Philippis on their connectedness. Together with an older resul t of McCann\, this answers positively the conjecture in dimension two. The proof is inspired by the two-point function technique introduced by B. An drews and is reminiscent of the doubling of variables trick in the context of viscosity solutions.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Filippo Santambrogio\, (Université Claude Bernard - Lyon 1) DTSTART:20200505T150000Z DTEND:20200505T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/3 DESCRIPTION:Title: Optimal transport methods for the regularity of 2D functions of least g radient\nby Filippo Santambrogio\, (Université Claude Bernard - Lyon 1) as part of Lisbon webinar in analysis and differential equations\n\n\nA bstract\nThe least gradient problem (minimizing the BV norm with given bou ndary data)\, motivated by both image processing applications and connecti ons with minimal surfaces\, is known to be equivalent\, in the plane\, to the Beckmann minimal-flow problem (an alternative formulation of the $L^1$ Monge-Kantorovich optimal transport problem) with source and target measu res located on the boundary of the domain. Hence\, Sobolev regularity of f unctions of least gradient is equivalent in this setting to $L^p$ bounds o n the solution of the Beckmann problem (i.e. on what is called the transpo rt density) and can be attacked with techniques which are now standard in optimal transport. From the transport point of view\, the novelty of the e stimates that I will present\, coming from a joint paper with S. Dweik\, l ies in the fact they are obtained for transport between measures which are concentrated on the boundary. From the BV point of view\, a new result is the $W^{1\,p}$ regularity of the least gradient function whenever the bou ndary datum is $W^{1\,p}$ as a 1D function: moreover\, the optimal transpo rt framework is strong enough to deal with arbitrary strictly convex norms instead of the Euclidean one with almost no effort.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo Oliveira e Silva (University of Birmingham) DTSTART:20200512T153000Z DTEND:20200512T163000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/4 DESCRIPTION:Title: Global maximizers for spherical restriction\nby Diogo Oliveira e Si lva (University of Birmingham) as part of Lisbon webinar in analysis and d ifferential equations\n\n\nAbstract\nWe prove that constant functions are the unique real-valued maximizers for all $L^2-L^{2n}$ adjoint Fourier res triction inequalities on the unit sphere $\\mathbb{S}^{d-1}\\subset\\mathb b{R}^d$\, $d\\in\\{3\,4\,5\,6\,7\\}$\, where $n\\geq 3$ is an integer. The proof uses tools from probability theory\, Lie theory\, functional analys is\, and the theory of special functions. It also relies on general soluti ons of the underlying Euler--Lagrange equation being smooth\, a fact of in dependent interest which we discuss. We further show that complex-valued m aximizers coincide with nonnegative maximizers multiplied by the character $e^{i\\xi\\cdot\\omega}$\, for some $\\xi$\, thereby extending previous w ork of Christ & Shao (2012) to arbitrary dimensions $d\\geq 2$ and general even exponents. This talk is based on results obtained with René Quilodr án.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernold Fiedler (Institute of Mathematics\, Freie Universität Ber lin) DTSTART:20200519T150000Z DTEND:20200519T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/5 DESCRIPTION:Title: Sturm meanders: global attractors\, Temperley-Lieb algebras\, and black holes\nby Bernold Fiedler (Institute of Mathematics\, Freie Universit ät Berlin) as part of Lisbon webinar in analysis and differential equatio ns\n\n\nAbstract\nFusco and Rocha studied Neumann boundary value problems for scalar ODEs of second order via a shooting approach. They introduced t he notion of what we now call Sturm permutations. These permutations relat e\, on the one hand\, to a special class of meandering curves as introduce d by Arnol’d in a singularity theory context. On the other hand\, they b ecame central in the study of global attractors of nonlinear parabolic par tial differential equations of Sturm type.\n\nWe discuss relations of Stur m meanders with further areas: the multiplicative and trace structure in T emperley-Lieb algebras\, discrete versions of Cartesian billiards\, and th e problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the lon g and meandric history of meander patterns themselves.\n\nWe report on joi nt work with Pablo Castañeda\, Juliette Hell\, Carlos Rocha\, and Brian S mith. See also http://dynamics.mi.fu-berlin.de/\n\nFor further material we recommend the beautifully illustrated book “Meanders” by Anna Karnauh ova\, de Gruyter 2017.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Vega (BCAM) DTSTART:20200526T150000Z DTEND:20200526T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/6 DESCRIPTION:Title: The Vortex Filament Equation\, the Talbot effect\, and non-circular jet s.\nby Luis Vega (BCAM) as part of Lisbon webinar in analysis and diff erential equations\n\n\nAbstract\nWe will propose the vortex filament equa tion as a possible toy model for turbulence\, in particular because of its striking similarity to the dynamics of non-circular jets. This similarity implies the existence of some type of Talbot effect due to the interactio n of non-linear waves that propagate along the filament. Another consequen ce of this interaction is the existence of a new class of multi-fractal se ts that can be seen as a generalization of the graph of Riemann’s non-di fferentiable function. Theoretical and numerical arguments about the trans fer of energy will be also given. This a joint work with V. Banica and F. de la Hoz.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Colombo (EPFL) DTSTART:20200602T150000Z DTEND:20200602T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/7 DESCRIPTION:Title: Nonunique characteristic curves of Sobolev vector fields\nby Maria Colombo (EPFL) as part of Lisbon webinar in analysis and differential equa tions\n\n\nAbstract\nGiven a vector field in $\\mathbb{R}^d$\, the classic al Cauchy-Lipschitz theorem shows existence and uniqueness of its flow pro vided the vector field is sufficiently smooth\; this\, in turn\, translate s in existence and uniqueness results for the transport equation. In 1989\ , Di Perna and Lions proved that Sobolev regularity for vector fields\, wi th bounded divergence and a growth assumption\, is sufficient to establish existence\, uniqueness and stability of a generalized notion of flow\, co nsisting of a suitable selection among the trajectories of the associated ODE. A long-standing open question is whether the uniqueness of the regula r Lagrangian flow is a corollaryof the uniqueness of the trajectory of the ODE for a.e. initial datum. In this talk we give an overview of the topic and we provide a negative answer to this question. To show this result we exploit the connection with the transport equation\, based on Ambrosio’ s superposition principle\, and a new ill-posedness result for positive so lutions of the continuity equation.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucio Boccardo (Università di Roma La Sapienza) DTSTART:20200609T150000Z DTEND:20200609T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/8 DESCRIPTION:Title: Recent developments on Dirichlet problems with singular convection/drif t terms\nby Lucio Boccardo (Università di Roma La Sapienza) as part o f Lisbon webinar in analysis and differential equations\n\n\nAbstract\nPle ase check https://wade.ulisboa.pt/seminars?id=5797\n LOCATION:https://researchseminars.org/talk/LisbonWADE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Adami (Politecnico di Torino) DTSTART:20200616T150000Z DTEND:20200616T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/9 DESCRIPTION:Title: Ground states of the Nonlinear Schroedinger Equation on Graphs: an over view\nby Riccardo Adami (Politecnico di Torino) as part of Lisbon webi nar in analysis and differential equations\n\n\nAbstract\nDriven by physic al and technological applications\, during the last five years the study o f nonlinear evolution on branched structures (graphs\, networks) has under gone a fast development. We review on the main achievements and on the ope n problems. This is a joint project with several people\, among which Simo ne Dovetta\, Enrico Serra\, Lorenzo Tentarelli\, and Paolo Tilli.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tatsuya Miura (Tokyo Institute of Technology) DTSTART:20200623T100000Z DTEND:20200623T110000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/10 DESCRIPTION:Title: On the isoperimetric inequality and surface diffusion flow for multipl y winding curves\nby Tatsuya Miura (Tokyo Institute of Technology) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstrac t\nIn this talk we discuss dynamical stability of multiply covered circles under the surface diffusion flow. To this end we first establish a genera l form of the isoperimetric inequality for immersed closed curves under ro tational symmetry\, which would be of independent interest. We then apply it to obtaining a certain class of rotationally symmetric initial curves f rom which solutions to the surface diffusion flow exist globally-in-time a nd converge to multiply covered circles. This talk is based on a joint wor k with Shinya Okabe at Tohoku University.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Brandolini (Università Degli Studi di Napoli Federico II) DTSTART:20200630T150000Z DTEND:20200630T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/11 DESCRIPTION:Title: Sharp lower bounds for Neumann eigenvalues.\nby Barbara Brandolini (Università Degli Studi di Napoli Federico II) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Elvira Zappale (Università Degli Studi di Salerno) DTSTART:20200709T150000Z DTEND:20200709T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/12 DESCRIPTION:Title: Optimal design problems\nby Elvira Zappale (Università Degli Stud i di Salerno) as part of Lisbon webinar in analysis and differential equat ions\n\n\nAbstract\nI will present several integral representation results for certain functionals arising in the context of optimal design and dama ge models\, in presence of a perimeter penalization term. I will consider several frameworks\, and I will also discuss the case with non-standard gr owth conditions.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie d Mathematics\, Prague) DTSTART:20200714T150000Z DTEND:20200714T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/13 DESCRIPTION:Title: Vertex coupling and spectra of periodic quantum graphs\nby Pavel E xner (Doppler Institute for Mathematical Physics and Applied Mathematics\, Prague) as part of Lisbon webinar in analysis and differential equations\ n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Baptiste Casteras (Universidade de Lisboa) DTSTART:20201022T133000Z DTEND:20201022T143000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/14 DESCRIPTION:Title: Standing wave and travelling wave solutions for a fourth order Schröd inger equation\nby Jean-Baptiste Casteras (Universidade de Lisboa) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstrac t\nIn this talk\, we will be interested in standing wave solutions to a fo urth order nonlinear Schrödinger equation having second and fourth order dispersion terms. This kind of equation naturally appears in nonlinear opt ics. In a first time\, we will establish the existence of ground-state and renormalized solutions. We will then be interested in their qualitative p roperties\, in particular their stability.\n\nJoint works with Denis Bonhe ure\, Ederson Moreira Dos Santos\, Tianxiang Gou\, Louis Jeanjean and Robs on Nascimento.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Chruściel & Lorenzo Mazzieri (University of Vienna / Univer sità di Trento) DTSTART:20201029T133000Z DTEND:20201029T143000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/15 DESCRIPTION:Title: Static vacuum black holes and Lambda\nby Piotr Chruściel & Lorenz o Mazzieri (University of Vienna / Università di Trento) as part of Lisbo n webinar in analysis and differential equations\n\n\nAbstract\nWe will re view the status of the uniqueness theory of static vacuum black holes\, wi th or without a cosmological constant $\\Lambda$\, and we will outline the proof of a uniqueness theorem with $\\Lambda>0$\, proved jointly in colla boration with Stefano Borghini.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Rainer Mandel (Karlsruhe Institute of Technology) DTSTART:20201112T143000Z DTEND:20201112T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/16 DESCRIPTION:Title: New dual variational methods for Nonlinear Helmholtz Equations and pol ychromatic solutions of Nonlinear wave equations\nby Rainer Mandel (Ka rlsruhe Institute of Technology) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nIn the first part of my talk\, I pr esent the classical dual variational method in the context of Nonlinear He lmholtz equations that describe monochromatic waves in nonlinear materials . Afterwards\, I discuss two recent generalizations of the method. The fir st deals with an extension to Nonlinear Helmholtz equations with sign-chan ging nonlinearities. For these problems we construct solutions that have i nfinite Morse-Index in the dual variational formulation. The second genera lization concerns dual variational methods for the construction of breathe rs\, i.e.\, polychromatic\, spatially localized and time-periodic solution s of nonlinear wave equations.\n\nThe results were obtained in collaborati on with D. Scheider and T. Yesil.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Youcef Mammeri (Université de Picardie Jules Verne) DTSTART:20201203T143000Z DTEND:20201203T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/17 DESCRIPTION:Title: A SIR-type model with diffusion to describe the spatial spread of Covi d-19\nby Youcef Mammeri (Université de Picardie Jules Verne) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe all have to deal with the coronavirus epidemic. Many strategies have been put in place to try to contain the disease\, with varying success.\nI wil l present an SIR-type mathematical model to predict the state of the epide mic. The effect of distancing\, isolation of exposed individuals and treat ment of symptoms will be compared. \nI will begin with a simple explanatio n of SIR models\, then discuss a PDE model and its resolution.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Wladimir Neves (Universidade Federal do Rio de Janeiro) DTSTART:20201105T143000Z DTEND:20201105T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/18 DESCRIPTION:Title: Homogenization of Schrödinger equations. Extended Effective Mass Theo rems for non-crystalline matter.\nby Wladimir Neves (Universidade Fed eral do Rio de Janeiro) as part of Lisbon webinar in analysis and differen tial equations\n\n\nAbstract\nIn this talk\, we study the homogenization o f the Schrödinger equation beyond the periodic setting. More precisely\, rigorous derivation of the effective \nmass theorems in solid state physic s for non-crystalline \nmaterials are obtained.\n\nThis is a joint work wi th Vernny Ccajma and Jean Silva.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Hynek Kovařík (Università degli studi di Brescia) DTSTART:20201116T143000Z DTEND:20201116T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/19 DESCRIPTION:Title: Absence of positive eigenvalues of magnetic Schroedinger operators \nby Hynek Kovařík (Università degli studi di Brescia) as part of Lisbo n webinar in analysis and differential equations\n\n\nAbstract\nWe study s ufficient conditions for the absence of positive eigenvalues of magnetic S chroedinger operators in $\\mathbb{R}^n$. In our main result we prove the absence of eigenvalues above certain threshold energy which depends explic itly on the magnetic and electric field. A comparison with the examples of Miller-Simon shows that our result is sharp as far as the decay of the ma gnetic field is concerned.\n\nThe talk is based on a joint work with Silva na Avramska-Lukarska and Dirk Hundertmark.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Caroccia (Università degli studi di Roma Tor Vergata) DTSTART:20201126T143000Z DTEND:20201126T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/20 DESCRIPTION:Title: Contact surface of Cheeger sets\nby Marco Caroccia (Università de gli studi di Roma Tor Vergata) as part of Lisbon webinar in analysis and d ifferential equations\n\n\nAbstract\nGeometrical properties of Cheeger set s have been deeply studied by many authors since their introduction\, as a way of bounding from below the first Dirichlet (p)-Laplacian eigenvualue. They represents the first eigenfunction of the Dirichlet (1)-Laplacian of a domain. In this talk we will introduce a recent property\, studied in c ollaboration with Simone Ciani\, concerning their contact surface with the ambient space. In particular we will show that the contact surface cannot be too small\, with a lower bound on the dimension strictly related to th e regularity of the ambient space. The talk will focus on the introduction of the problem and with a brief explanation of its connection with the Di richlet (p)-Laplacian eigenvalue problem. Then a brief sketch of the proof is given. Functional to the whole argument is the notion of removable sin gularity\, as a tool for extending solutions of pdes under some regularity constraint.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Qiao Huang (GFM\, University of Lisbon) DTSTART:20201210T143000Z DTEND:20201210T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/21 DESCRIPTION:Title: Stochastic Cucker-Smale model: collision-avoidance and flocking\nb y Qiao Huang (GFM\, University of Lisbon) as part of Lisbon webinar in ana lysis and differential equations\n\n\nAbstract\nIn this talk\, we consider the Cucker-Smale flocking model involving both singularity and noise. We first show the local strong well-posedness for the system\, in which the c ommunication weight is locally Lipschitz beyond the origin. Then\, for the special case that the communication weight has a strong singularity at th e origin\, we establish the global well-posedness by showing the finite ti me collision-avoidance. Finally\, we study the large time behavior of the system when the communication weight is of zero lower bound. The condition al flocking emerges for the case of constant noise intensity\, while the u nconditional flocking emerges for various time-varying intensities and lon g-range communications.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Francois Babadjian (Université Paris Saclay) DTSTART:20201126T133000Z DTEND:20201126T143000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/22 DESCRIPTION:Title: Concentration versus oscillation effects in brittle damage\nby Jea n-Francois Babadjian (Université Paris Saclay) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nThis talk is concern ed with the asymptotic analysis of a variational model of brittle damage\, when the damaged zone concentrates into a set of zero Lebesgue measure\, and\, at the same time\, the stiffness of the damaged material becomes arb itrarily small. In a particular non-trivial regime\, concentration leads t o a limit energy with linear growth as typically encountered in perfect pl asticity. While the singular part of the limit energy can be easily descri bed\, the identification of the bulk part of the limit energy requires a s ubtler analysis of the interplay between concentration and oscillation pro perties of the displacements.\nThis is a joint work with F. Iurlano and F. Rindler.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Svetlana Roudenko (Florida International University) DTSTART:20201217T143000Z DTEND:20201217T153000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/23 DESCRIPTION:Title: Zakharov-Kuznetsov equation: toward soliton resolution\nby Svetlan a Roudenko (Florida International University) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe consider Zakharov-K uznetsov (ZK) equation\, which is a higher-dimensional version of the Kort eweg-de Vries (KdV) equation\, and investigate the dynamics of solutions\, especially questions about the soliton stability. We first discuss the si tuation in two dimensions\, in particular\, the instability of solitons in the 2d cubic (critical) ZK equation\, which leads to blow-up. Then we con sider the 3d quadratic ZK equation\, originally introduced by Zakharov and Kuznetsov in early 1970's\, and discuss the asymptotic stability of solit ons. We will also show numerical findings on the formation of solitons and radiation in this equation. This talk will be based on joint works with L .G. Farah\, J. Holmer\, C. Klein\, N. Stoilov\, K. Yang.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Nilima Nigam (Simon Fraser University) DTSTART:20210107T163000Z DTEND:20210107T173000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/24 DESCRIPTION:Title: Boundary integral strategies for the Steklov eigenproblem\nby Nili ma Nigam (Simon Fraser University) as part of Lisbon webinar in analysis a nd differential equations\n\n\nAbstract\nIn Steklov eigenproblems for elli ptic operators\, the spectral parameter links boundary traces of eigenfunc tions to traces of the Neumann data. It is natural\, therefore\, to reform ulate such eigenproblems in terms of boundary integral operators\, which a llow for nonsmooth boundaries. In this talk we describe such strategies in the context of Steklov problems for the Laplacian as well as the Helmholt z operator\, and their use in studying questions arising in spectral geome try.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Serena Dipierro & Enrico Valdinoci (University of Western Australi a) DTSTART:20210114T100000Z DTEND:20210114T120000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/25 DESCRIPTION:Title: Nonlocal Minimal Surfaces: interior regularity\, boundary behavior and stickiness phenomena\nby Serena Dipierro & Enrico Valdinoci (Universi ty of Western Australia) as part of Lisbon webinar in analysis and differe ntial equations\n\n\nAbstract\nSurfaces which minimize a nonlocal perimete r functional exhibit quite different behaviors than the ones minimizing th e classical perimeter. We will investigate some structural properties of n onlocal minimal surfaces both in the interior of a given domain and in the vicinity of its boundary.\nAmong these peculiar features\, an interesting property\, which is also in contrast with the pattern produced by the sol utions of linear equations\, is given by the capacity\, and the strong ten dency\, of adhering at the boundary. We will also discuss this phenomenon and present some recent results.\n\n(these are two consecutive talks: Part I is given by Serena Dipierro\, Part II by Enrico Valdinoci)\n LOCATION:https://researchseminars.org/talk/LisbonWADE/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Collot (Cergy Paris Université) DTSTART:20210121T140000Z DTEND:20210121T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/26 DESCRIPTION:Title: On the stability of equilibria for infinitely many particles\nby C harles Collot (Cergy Paris Université) as part of Lisbon webinar in analy sis and differential equations\n\n\nAbstract\nWe study the evolution of a system of particles. Instead of the usual Hartree equation for density mat rices\, we consider the following equivalent model\, proposed by de Suzzon i\, of a Hartree type equation but for a random field:$$iX_t=-\\Delta X +( w*\\mathbb E(|X|^2))X.$$Above\, $X:[0\,T]\\times \\mathbb R^d\\times \\Ome ga$ is a time-dependent random field\, $w$ a pair interaction potential\, $*$ the convolution product and $\\mathbb E$ the expectation. This equatio n admits equilibria which are random Gaussian fields whose laws are invari ant by time and space translations. They are hence not localised and repre sent an infinite number of particles. We give a stability result under cer tain hypotheses\, by showing that small perturbations scatter as $t\\right arrow \\pm \\infty$ to linear waves. This is joint work with de Suzzoni.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrico Serra (Politecnico di Torino) DTSTART:20210128T140000Z DTEND:20210128T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/27 DESCRIPTION:Title: NLS ground states on metric trees: existence results and open question s\nby Enrico Serra (Politecnico di Torino) as part of Lisbon webinar i n analysis and differential equations\n\n\nAbstract\nWe consider the minim ization of the NLS energy on a metric tree\, either rooted or unrooted\, s ubject to a mass constraint. With respect to the same problem on other typ es of metric graphs\, several new features appear\, such as the existence of minimizers with positive energy\, and the emergence of unexpected thres hold phenomena. We also study the problem with a radial symmetry constrain t that is in principle different from the free problem due to the failure of the Polya-Szego inequality for radial rearrangements. A key role is pla yed by a new Poincaré inequality with remainder.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Boyan Sirakov (PUC - Rio) DTSTART:20210225T140000Z DTEND:20210225T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/28 DESCRIPTION:Title: The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients\nby Boyan Sirakov (PUC - Rio) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nIn this joint work with P. Souplet we develop a new\, unified approach to th e following two classical questions on elliptic PDE:\n(i) the strong maxim um principle for equations with non-Lipschitz nonlinearities\; and\n(ii) t he at most exponential decay of solutions in the whole space or exterior d omains.\n\nOur results apply to divergence and nondivergence operators wit h locally unbounded lower-order coefficients\, in a number of situations w here all previous results required bounded ingredients. Our approach\, whi ch allows for relatively simple and short proofs\, is based on a (weak) Ha rnack inequality with optimal dependence of the constants in the lower-ord er terms of the equation and the size of the domain\, which we establish.\ n LOCATION:https://researchseminars.org/talk/LisbonWADE/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Yvan Martel (École Polytechnique) DTSTART:20210204T140000Z DTEND:20210204T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/29 DESCRIPTION:Title: On the asymptotic stability of kinks for (1+1)-scalar field models \nby Yvan Martel (École Polytechnique) as part of Lisbon webinar in analy sis and differential equations\n\n\nAbstract\n

The talk concerns stabili ty properties of kinks for (1+1)-dimensional nonlinear scalar field models of the form
\\[\\partial_t^2 \\phi - \\partial_x^2 \\phi + W'(\\phi) = 0 \\quad (t\,x) \\in {\\bf R}\\times {\\bf R}.\\]
We establish a s imple and explicit sufficient condition on the potential $W$ for the asymp totic stability of a given moving or standing kink.
We present applic ations of the criterion to some models of the Physics literature.

Wo rk in collaboration with Michał Kowalczyk\, Claudio Muñoz and Hanne Van Den Bosch

https://arxiv.o rg/abs/2008.01276

See also the related work with Michał Kowalcz yk and Claudio Muñoz

htt ps://arxiv.org/abs/1903.12460

\n LOCATION:https://researchseminars.org/talk/LisbonWADE/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Bozhidar Velichkov (Università di Pisa) DTSTART:20210304T140000Z DTEND:20210304T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/30 DESCRIPTION:Title: Vectorial free boundary problems\nby Bozhidar Velichkov (Universit à di Pisa) as part of Lisbon webinar in analysis and differential equatio ns\n\n\nAbstract\nThe vectorial Bernoulli problem is a variational free bo undary problem involving the Dirichlet energy of a vector-valued function and the measure of its support. It is the vectorial counterpart of the cla ssical one-phase Bernoulli problem\, which was first studied by Alt and Ca ffarelli in 1981.\n\nIn this talk\, we will discuss some results on the re gularity of the vectorial free boundaries obtained in the last years by Ca ffarelli-Shahgholian-Yeressian\, Kriventsov-Lin\, Mazzoleni-Terracini-V.\, and Spolaor-V.. Finally\, we will present some new results on the rectifi ability of the singular set obtained in collaboration with Guido De Philip pis\, Max Engelstein and Luca Spolaor.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Dario Mazzoleni (Università di Pavia) DTSTART:20210304T150000Z DTEND:20210304T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/31 DESCRIPTION:Title: Regularity of the optimal sets for the second Dirichlet eigenvalue \nby Dario Mazzoleni (Università di Pavia) as part of Lisbon webinar in a nalysis and differential equations\n\n\nAbstract\nFirst of all\, we recall the basic notions and results concerning shape optimization problems for the eigenvalues of the Dirichlet Laplacian.\nThen we focus on the study of the regularity of the optimal shapes and on the link with the regularity of related free boundary problems.\n\nThe main topic of the talk is the re gularity of the optimal sets for a "degenerate'" functional\, namely the s econd Dirichlet eigenvalue in a box. Given $D\\subset \\mathbb{R}^d$ an op en and bounded set of class $C^{1\,1}$\, we consider the following shape o ptimization problem\, for $\\Lambda>0$\,\\begin{equation}\\label{eq:main}\ \min{\\Big\\{\\lambda_2(A)+\\Lambda |A| : A\\subset D\,\\text{ open}\\Big\ \}}\,\\end{equation}where $\\lambda_2(A)$ denotes the second eigenvalue of the Dirichlet Laplacian on $A$.\n\nIn this talk we show that any optimal set $\\Omega$ for \\eqref{eq:main} is equivalent to the union of two disjo int open sets\, $\\Omega^\\pm$\, which are $C^{1\,\\alpha}$ regular up to a (possibly empty) closed singular set of Hausdorff dimension at most $d-5 $\, which is contained in the one-phase free boundaries.\n\nIn particular\ , we are able to prove that the set of two-phase points\, that is\, $\\par tial \\Omega^+\\cap \\partial \\Omega^-\\cap D$\, is contained in the regu lar set.\n\n\nThis is a joint work with Baptiste Trey and Bozhidar Velichk ov.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriele Benomio (Princeton University) DTSTART:20210318T140000Z DTEND:20210318T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/32 DESCRIPTION:Title: A new instability for higher dimensional black holes\nby Gabriele Benomio (Princeton University) as part of Lisbon webinar in analysis and d ifferential equations\n\n\nAbstract\nThe dynamics of solutions to the Eins tein equations is richer in dimensions higher than $3+1$. In contrast with the classical stability of stationary\, asymptotically flat black hole so lutions in $3+1$ dimensions\, some families of higher dimensional black ho les suffer from dynamical instabilities. I will discuss a subtle instabili ty affecting a wide class of higher dimensional black holes which has not been previously observed in the literature. This new instability is\, in a sense\, more fundamental than the other known instability phenomena in hi gher dimensions and can be related to a precise geometric property of the class of spacetimes considered.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Shrish Parmeshwar (University of Bath) DTSTART:20210318T150000Z DTEND:20210318T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/33 DESCRIPTION:Title: Global-in-Time Solutions to the N-Body Euler-Poisson System\nby Sh rish Parmeshwar (University of Bath) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe investigate the $N$-Body com pressible Euler-Poisson system\, modelling multiple stars interacting with each other via Newtonian gravity. If we prescribe initial data so that ea ch star expands indefinitely\, one might expect that two of them will coll ide in finite time due to their expansion\, and the influence of gravity. In this talk we show that there exists a large family of initial positions and velocities for the system such that each star can expand for all time \, but no two will touch in finite time. To do this we use scaling mechani sms present in the compressible Euler system\, and a careful analysis of h ow the gravitational interaction between stars affects their dynamics.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Harbir Antil (George Mason University) DTSTART:20210211T140000Z DTEND:20210211T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/34 DESCRIPTION:Title: Fractional PDEs: Control\, Numerics\, and Applications\nby Harbir Antil (George Mason University) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nFractional calculus and its applicat ion to anomalous diffusion has recently received a tremendous amount of at tention. In complex/heterogeneous material mediums\, the long-range correl ations or hereditary material properties are presumed to be the cause of s uch anomalous behavior. Owing to the revival of fractional calculus\, thes e effects are now conveniently modeled by fractional-order differential op erators and the governing equations are reformulated accordingly. Similarl y\, the potential of fractional operators has been harnessed in various sc ientific domains like geophysical electromagnetics\, imaging science\, dee p learning\, etc. \n\nIn this talk\, fractional operators will be introdu ced and both linear and nonlinear\, fractional-order differential equation s will be discussed. New notions of optimal control and optimization under uncertainty will be presented. Several applications from geophysics\, ima ging science\, and deep learning will be presented.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Gidoni (Czech Academy of Sciences) DTSTART:20210218T140000Z DTEND:20210218T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/35 DESCRIPTION:Title: A vanishing inertia analysis for finite dimensional rate-independent s ystems and an application to soft crawlers\nby Paolo Gidoni (Czech Aca demy of Sciences) as part of Lisbon webinar in analysis and differential e quations\n\n\nAbstract\nThe quasistatic limit is a convenient approximatio n in the modelling of several (suitable) mechanical systems\, when the evo lution occurs at a sufficiently slow time-scale. In this talk we discuss t he validity of the quasistatic approximation in finite-dimensional rate-in dependent systems via a vanishing-inertia asymptotic analysis of dynamic e volutions. More precisely\, we show the uniform convergence of dynamic sol utions to the quasistatic one\, employing the concept of energetic solutio n. Our work is motivated by the application to a family of models for biol ogical and bio-inspired crawling locomotion. Hence a part of the seminar w ill focus on modelling: we will discuss how soft crawlers can be effective ly described in our theoretical framework and briefly survey the relevance \, or lack thereof\, of inertia in some locomotion strategies. By a techni cal point of view\, our application requires time-dependence of the dissip ation potential and translation invariance of the potential energy. \n\nJo int work with Filippo Riva (http://arxiv.org/abs/2007.09069 ).\n LOCATION:https://researchseminars.org/talk/LisbonWADE/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Premoselli (Université Libre de Bruxelles) DTSTART:20210311T140000Z DTEND:20210311T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/36 DESCRIPTION:Title: Towers of bubbles for Yamabe-type equations in dimensions larger than 7\nby Bruno Premoselli (Université Libre de Bruxelles) as part of Lis bon webinar in analysis and differential equations\n\n\nAbstract\nIn this talk we consider perturbations of Yamabe-type equations on closed Riemanni an manifolds. In dimensions larger than 7 and on locally conformally flat manifolds we construct blowing-up solutions that behave like towers of bub bles concentrating at a critical point of the mass function. Our result do es not assume any symmetry on the underlying manifold.\n\nWe perform our c onstruction by combining finite-dimensional reduction methods with a linea r blow-up analysis in order to sharply control the remainder of the constr uction in strong spaces. Our approach works both in the positive and sign- changing case. As an application we prove the existence\, on a generic bou nded open set of $\\mathbb{R}^n$\, of blowing-up solutions of the Brézis- Nirenberg equation that behave like towers of bubbles of alternating signs .\n LOCATION:https://researchseminars.org/talk/LisbonWADE/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria Chiadò Piat (Politecnico di Torino) DTSTART:20210408T130000Z DTEND:20210408T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/37 DESCRIPTION:Title: An extension theorem from connected sets and homogenization of non-loc al functionals\nby Valeria Chiadò Piat (Politecnico di Torino) as par t of Lisbon webinar in analysis and differential equations\n\n\nAbstract\n Extensions operators are a classical tool to provide uniform estimates and gain compactness in the homogenization of integral functionals over perfo rated domains. In this talk we discuss the case of non-local functionals. The results are obtained in collaboration with Andrea Braides and Lorenza D'Elia.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Fusco (Università di Napoli "Federico II") DTSTART:20210415T130000Z DTEND:20210415T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/38 DESCRIPTION:Title: Asymptotic stability for the gradient flow of some nonlocal energies\nby Nicola Fusco (Università di Napoli "Federico II") as part of Lisbo n webinar in analysis and differential equations\n\n\nAbstract\nI will sta rt by discussing some recent results on the asymptotic stability of the $H ^{-1}$-gradient flow of the perimeter\, the so called surface diffusion. T hen I will consider the $H^{-1}$-gradient flow of some energy functionals given by the area of an interface plus a non local volume term. This is a joint work with E. Acerbi\, V. Julin and M. Morini\n LOCATION:https://researchseminars.org/talk/LisbonWADE/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Grégoire Allaire (CMAP\, Ecole Polytechnique) DTSTART:20210401T130000Z DTEND:20210401T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/39 DESCRIPTION:Title: Some problems and some solutions in shape and topology optimization of structures built by additive manufacturing\nby Grégoire Allaire (CMA P\, Ecole Polytechnique) as part of Lisbon webinar in analysis and differe ntial equations\n\n\nAbstract\nAdditive manufacturing (or 3-d printing) is a new exciting way of building structures without any restriction on thei r topologies. However\, it comes with its own difficulties or new issues. Therefore\, it is a source of many interesting new problems for optimizati on. I shall discuss two of them and propose solutions to these problems\, but there is still a lot of room for improvement!\n\nFirst\, additive manu facturing technologies are able to build finely graded microstructures (ca lled lattice materials). Their optimization is therefore an important issu e but also an opportunity for the resurrection of the homogenization metho d ! Indeed\, homogenization is the right technique to deal with microstruc tured materials where anisotropy plays a key role\, a feature which is abs ent from more popular methods\, like SIMP. I will describe recent work on the topology optimization of these lattice materials\, based on a combinat ion of homogenization theory and geometrical methods for the overall defor mation of the lattice grid.\n\nSecond\, additive manufacturing\, especiall y in its powder bed fusion technique\, is a very slow process because a la ser beam must travel along a trajectory\, which covers the entire structur e\, to melt the powder. Therefore\, the optimization of the laser path is an important issue. Not only do we propose an optimization strategy for th e laser path\, but we couple it with the usual shape and topology optimiza tion of the structure. Numerical results show that these two optimizations are tightly coupled.\n\nThis is a joint work with many colleagues\, inclu ding two former PhD students\, P. Geoffroy-Donders and M. Boissier.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Scala (Università degli Studi di Siena) DTSTART:20210415T140000Z DTEND:20210415T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/40 DESCRIPTION:Title: Nonlocality features of the area functional and the Plateau problem\nby Riccardo Scala (Università degli Studi di Siena) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe briefly d iscuss the definition of relaxation of the area functional. The relaxed ar ea functional\, denoted by $A$\, extends the classical area functional\, w hich\, for any "regular" map $v:U\\subset \\mathbb{R}^n\\rightarrow \\math bb{R}^N$ evaluates the $n$-dimensional area of its graph over $U$. The pro blem of determining the domain and the expression of $A$ is open in codime nsion greater than 1. Specifically\, this relaxed functional turns out to be nonlocal and cannot be expressed by an integral formula. We discuss how it is related to classical and nonclassical versions of the Plateau probl em. As a main example\, we try to understand what is the relaxed graph of the function $x/|x|$\, a question that surprisingly remained open for deca des.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Yukihiko Nakata (Aoyama Gakuin University) DTSTART:20210325T140000Z DTEND:20210325T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/41 DESCRIPTION:Title: Period two solution for a class of distributed delay differential equa tions\nby Yukihiko Nakata (Aoyama Gakuin University) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe consider a periodic solution for a class of distributed delay differential equatio ns.\n\nA period two solution for distributed delay differential equations\ , where the period is twice the maximum delay\, is shown to satisfy a Hami ltonian system of ordinary differential equations\, from which we can cons truct the period two solution for the distributed delay differential equat ion.\n\nThe idea is based on Kaplan & Yorke (1974\, JMAA) for a discrete d elay differential equation. We present distributed delay differential equa tions that have periodic solutions expressed in terms of the Jacobi ellipt ic functions.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Luis Vásquez (Universidad Autónoma de Madrid) DTSTART:20210422T130000Z DTEND:20210422T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/42 DESCRIPTION:Title: The theory of fractional p-Laplacian equations\nby Juan Luis Vásq uez (Universidad Autónoma de Madrid) as part of Lisbon webinar in analysi s and differential equations\n\n\nAbstract\nWe consider the time-dependent fractional p-Laplacian equation with parameter $p>1$ and fractional expon ent $0Homogenisation of discrete dynamical optimal transport\nby Jan Mas s (IST Austria) as part of Lisbon webinar in analysis and differential equ ations\n\n\nAbstract\nMany stochastic systems can be viewed as gradient fl ow ('steepest descent') in the space of probability measures\, where the d riving functional is a relative entropy and the relevant geometry is descr ibed by a dynamical optimal transport problem. In this talk we focus on th ese optimal transport problems and describe recent work on the limit passa ge from discrete to continuous.\nSurprisingly\, it turns out that discrete transport metrics may fail to converge to the expected limit\, even when the associated gradient flows converge. We will illustrate this phenomenon in examples and present a recent homogenisation result.\n\nThis talk is b ased on joint work with Peter Gladbach\, Eva Kopfer\, and Lorenzo Portinal e.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Fathi (Université de Paris) DTSTART:20210429T140000Z DTEND:20210429T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/44 DESCRIPTION:Title: A proof of the Caffarelli contraction theorem via entropic interpolati on\nby Max Fathi (Université de Paris) as part of Lisbon webinar in a nalysis and differential equations\n\n\nAbstract\nThe Caffarelli contracti on theorem states that optimal transport maps (for the quadratic cost) fro m a Gaussian measure onto measures that satisfy certain convexity properti es are globally Lipschitz\, with a dimension-free estimate. It has found m any applications in probability\, such as concentration and functional ine qualities. In this talk\, I will present an alternative proof\, using entr opic interpolation and variational arguments. Joint work with Nathael Gozl an and Maxime Prod'homme.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone DiMarino (Università di Genova) DTSTART:20210513T130000Z DTEND:20210513T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/45 DESCRIPTION:by Simone DiMarino (Università di Genova) as part of Lisbon w ebinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Didier Pilod (University of Bergen) DTSTART:20210506T130000Z DTEND:20210506T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/46 DESCRIPTION:Title: Global well-posedness and scattering for the Dysthe equation in $L^2(\ \mathbb{R}^2)$\nby Didier Pilod (University of Bergen) as part of Lisb on webinar in analysis and differential equations\n\n\nAbstract\nThe Dysth e equation is a higher order approximation of the water waves system in th e modulation (Schrödinger) regime and in the infinite depth case. After r eviewing the derivation of the Dysthe and related equations\, we will focu s on the initial-value problem. We prove a small data global well-posednes s and scattering result in the critical space $L^2(\\mathbb R^2)$. This re sult is sharp in view of the fact that the flow map cannot be $C^3$ contin uous below $L^2(\\mathbb R^2)$.\n\nOur analysis relies on linear and bilin ear Strichartz estimates in the context of the Fourier restriction norm me thod. Moreover\, since we are at a critical level\, we need to work in the framework of the atomic space $U^2_S $ and its dual $V^2_S $ of square bo unded variation functions.\n\nWe also prove that the initial-value problem is locally well-posed in $H^s(\\mathbb R^2)$\, $s\\gt 0$.\n\nOur results extend to the finite depth version of the Dysthe equation.\nThis talk is b ased on a joint work with Razvan Mosincat (University of Bergen) and Jean- Claude Saut (Université Paris-Saclay).\n LOCATION:https://researchseminars.org/talk/LisbonWADE/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariana Smit Vega Garcia (Western Washington University) DTSTART:20210520T130000Z DTEND:20210520T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/47 DESCRIPTION:Title: Regularity of almost minimizers with free boundary\nby Mariana Smi t Vega Garcia (Western Washington University) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe study almost minimi zer for functionals that yield a free boundary\, as in the work of Alt-Caf farelli and Alt-Caffarelli-Friedman. The almost minimizing property can be understood as the defining characteristic of a minimizer in a problem tha t explicitly takes noise into account. In this talk\, we discuss the regul arity of almost minimizers to energy functionals with variable coefficient s. This is joint work with Guy David\, Max Engelstein & Tatiana Toro.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Julio D. Rossi (Universidad de Buenos Aires) DTSTART:20210527T130000Z DTEND:20210527T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/48 DESCRIPTION:Title: Non Linear Mean Value Properties for Monge-Ampère Equations\nby J ulio D. Rossi (Universidad de Buenos Aires) as part of Lisbon webinar in a nalysis and differential equations\n\n\nAbstract\nIn recent years there ha s been an increasing interest in whether a mean value property\, known to characterize harmonic functions\, can be extended in some weak form to sol utions of nonlinear equations. This question has been partially motivated by the surprising connection between Random Tug-of-War games and the norm alized $p-$Laplacian discovered some years ago\, where a nonlinear asympto tic mean value property for solutions of a PDE is related to a dynamic pro gramming principle for an appropriate game.\nOur goal in this talk is to show that an asymptotic nonlinear mean value formula holds for the classic al Monge-Ampère equation.\nJoint work with P. Blanc (Jyvaskyla)\, F. Char ro (Detroit)\, and J.J. Manfredi (Pittsburgh).\n LOCATION:https://researchseminars.org/talk/LisbonWADE/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael Benguria (PUC Chile) DTSTART:20210930T130000Z DTEND:20210930T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/49 DESCRIPTION:Title: Gagliardo-Nirenberg-Sobolev Inequalities and their counterparts on bou nded domains\nby Rafael Benguria (PUC Chile) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Monica Clapp (Universidad Nacional Autónoma de México) DTSTART:20211007T130000Z DTEND:20211007T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/50 DESCRIPTION:Title: Optimal partitions for the Yamabe equation\nby Monica Clapp (Unive rsidad Nacional Autónoma de México) as part of Lisbon webinar in analysi s and differential equations\n\n\nAbstract\nThe Yamabe equation on a Riema nnian manifold $(M\,g)$ is relevant to the question of finding a constant scalar curvature metric on $M$ that is conformally equivalent to the given one.\n\nAn optimal $\\ell$-partition for the Yamabe equation is a cover o f $M$ by $\\ell$ pairwise disjoint open subsets such that the Yamabe equat ion with Dirichlet boundary condition has a least energy solution on each one of these sets\, and the sum of the energies of these solutions is mini mal.\n\nWe will present some recent results obtained in collaboration with Angela Pistoia (La Sapienza Università di Roma) and Hugo Tavares (Univer sidade de Lisboa) that establish the existence and qualitative properties of such partitions.\n\nIf time allows\, we will also present some results on symmetric optimal partitions obtained in collaboration with Angela Pist oia\, and with Alberto Saldaña (UNAM) and Andrzej Szulkin (Stockholm Univ ersity).\n LOCATION:https://researchseminars.org/talk/LisbonWADE/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Juraj Földes (University of Virginia) DTSTART:20211014T150000Z DTEND:20211014T160000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/51 DESCRIPTION:Title: Stochastic approach to boundary regularity of hypoelliptic PDEs\nb y Juraj Földes (University of Virginia) as part of Lisbon webinar in anal ysis and differential equations\n\n\nAbstract\nWe will discuss the almost sure behavior of solutions of stochastic differential equations(SDEs) as t ime goes to zero. Our main general result establishes a functional law of the iterated logarithm (LIL) that applies in the setting of SDEs with dege nerate noise satisfying the weak Hormander condition. We will introduce la rge deviations to provide some details of proofs. Furthermore\, we apply t he stochastic results to the problem of identifying regular points for hyp oelliptic diffusions and obtain criteria for well posedness of degenerate equations.\n\nThis is a joint work with David Herzog and Marco Carfagnini\ n LOCATION:https://researchseminars.org/talk/LisbonWADE/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Dovetta (Università degli Studi di Roma "La Sapienza") DTSTART:20211021T130000Z DTEND:20211021T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/52 DESCRIPTION:Title: Action versus energy ground states in nonlinear Schrödinger equations \nby Simone Dovetta (Università degli Studi di Roma "La Sapienza") as part of Lisbon webinar in analysis and differential equations\n\n\nAbstra ct\nThe talk investigates the relations between normalized critical points of the nonlinear Schrödinger energy functional and critical points of th e corresponding action functional on the associated Nehari manifold.\n\nFi rst\, we show that the ground state levels are strongly related by the fol lowing duality result: the (negative) energy ground state level is the Leg endre—Fenchel transform of the action ground state level. Furthermore\, whenever an energy ground state exists at a certain frequency\, then all a ction ground states with that frequency have the same mass and are energy ground states too. We see that the converse is in general false and that t he action ground state level may fail to be convex. Next we analyze the di fferentiability of the ground state action level and we provide an explici t expression involving the mass of action ground states. Finally we show t hat similar results hold also for local minimizers\, and we exhibit exampl es of domains where our results apply.\n\nThe matter of the talk refers to joint works with Enrico Serra and Paolo Tilli.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Kelei Wang (Wuhan University) DTSTART:20211104T140000Z DTEND:20211104T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/53 DESCRIPTION:Title: Regularity of transition layers in Allen-Cahn equation\nby Kelei W ang (Wuhan University) as part of Lisbon webinar in analysis and different ial equations\n\n\nAbstract\nIn this talk I will survey the regularity the ory for transition layers in singularly perturbed Allen-Cahn equation\, fr om zeroth order regularity to second order one. Some applications of this regularity theory will also be discussed\, including De Giorgi conjecture\ , classification of finite Morse index solutions and construction of minim al hypersurfaces by Allen-Cahn approximation.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Bellettini (ICTP and Università di Siena) DTSTART:20211118T140000Z DTEND:20211118T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/54 DESCRIPTION:Title: On a conjecture of De Giorgi on the first variation of the Modica-Mort ola functional\nby Giovanni Bellettini (ICTP and Università di Siena) as part of Lisbon webinar in analysis and differential equations\n\n\nAbs tract\nWe shall discuss some (not so recent) results on a 1991 conjecture of De Giorgi concerning the Gamma limit of the square norm of the first va riation of the Modica-Mortola functionals\, and its relation with the Will more functional.\n LOCATION:https://researchseminars.org/talk/LisbonWADE/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Van Schaftingen (Université Catholique de Louvain) DTSTART:20211202T140000Z DTEND:20211202T150000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/55 DESCRIPTION:Title: Ginzburg-Landau functionals on planar domains for a general compact va cuum manifold\nby Jean Van Schaftingen (Université Catholique de Louv ain) as part of Lisbon webinar in analysis and differential equations\n\n\ nAbstract\n**PostPoned**\n LOCATION:https://researchseminars.org/talk/LisbonWADE/55/ END:VEVENT BEGIN:VEVENT SUMMARY:João Pedro Ramos (ETH Zurich) DTSTART:20220615T130000Z DTEND:20220615T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/56 DESCRIPTION:Title: Time-frequency localisation operators\, their eigenvalues and relation ship to elliptic PDE\nby João Pedro Ramos (ETH Zurich) as part of Lis bon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Kuksin (Univ. Paris VII) DTSTART:20220617T100000Z DTEND:20220617T110000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/57 DESCRIPTION:Title: Kolmogorov theory of turbulence and a rigorous theory of one-dimension al turbulence\nby Sergei Kuksin (Univ. Paris VII) as part of Lisbon we binar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Marroquin (Universidade Federal do Rio de Janeiro) DTSTART:20220628T130000Z DTEND:20220628T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/58 DESCRIPTION:Title: Stochastic two-scale Young measures and homogenization of conservation laws with multiplicative noise\nby Daniel Marroquin (Universidade Fed eral do Rio de Janeiro) as part of Lisbon webinar in analysis and differen tial equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Hermano Frid (Instituto de Matemática Pura e Aplicada) DTSTART:20220629T130000Z DTEND:20220629T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/59 DESCRIPTION:Title: On short wave-long wave interactions in the relativist context\nby Hermano Frid (Instituto de Matemática Pura e Aplicada) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Jörg Wolf (Chung-Ang University) DTSTART:20220721T130000Z DTEND:20220721T140000Z DTSTAMP:20260404T085124Z UID:LisbonWADE/60 DESCRIPTION:Title: Existence of weak solutions the equations of a non-Newtonian fluid wit h non standard growth\nby Jörg Wolf (Chung-Ang University) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LisbonWADE/60/ END:VEVENT END:VCALENDAR