BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Camillo De Lellis (IAS\, Princeton) DTSTART:20200415T200000Z DTEND:20200415T210000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/1 DESCRIPTION:Title: Flows of vector fields: classical and modern\nby Camillo De Lellis (IA S\, Princeton) as part of Rio de Janeiro webinar on analysis and partial d ifferential equations\n\n\nAbstract\nConsider a (possibly time-dependent) vector field $v$ on the Euclidean space. The classical Cauchy-Lipschitz (a lso named Picard-Lindel\\"of) Theorem states that\, if the vector field $v $ is Lipschitz in space\, for every initial datum $x$ there is a unique tr ajectory $\\gamma$ starting at $x$ at time $0$ and solving the ODE $\\dot{ \\gamma} (t) = v (t\, \\gamma (t))$. The theorem looses its validity as so on as $v$ is slightly less regular. However\, if we bundle all trajectorie s into a global map allowing $x$ to vary\, a celebrated theory put forward by DiPerna and Lions in the 80es show that there is a unique such flow un der very reasonable conditions and for much less regular vector fields. A long-standing open question is whether this theory is the byproduct of a s tronger classical result which ensures the uniqueness of trajectories for {\\em almost every} initial datum. I will give a complete answer to the la tter question and draw connections with partial differential equations\, h armonic analysis\, probability theory and Gromov's $h$-principle.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo A. Gomes (KAUST) DTSTART:20200422T120000Z DTEND:20200422T130000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/2 DESCRIPTION:Title: A mean-field price model\nby Diogo A. Gomes (KAUST) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstra ct\nWe propose a mean-field game model for the price formation of a commod ity whose production is subjected to deterministic or random fluctuations. Agents seek to minimize their average cost by choosing their trading rate s with a price that is characterized by a balance between supply and deman d. In the deterministic case\, we establish the existence of a solution un der general conditions and give a full characterization. In the stochastic case\, we show that\, for linear dynamics and quadratic costs\, the optim al trading rates are determined in feedback form. Hence\, the price arises as the solution to a stochastic differential equation\, whose coefficient s depend on the solution of a system of ordinary differential equations.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiana De Filippis (Oxford) DTSTART:20200429T130000Z DTEND:20200429T140000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/3 DESCRIPTION:Title: Vectorial problems: sharp Lipschitz bounds and borderline regularity\n by Cristiana De Filippis (Oxford) as part of Rio de Janeiro webinar on ana lysis and partial differential equations\n\n\nAbstract\nFor the abstract o f Cristiana's talk\, please use the following link: \n\nhttps://drive.goog le.com/open?id=1eU6lWvs808FKxdqswC2x3JPJ2jEmMgFz\n\nTo join the webinar\, use the following information:\n\nLink:\n\nhttps://puc-rio.zoom.us/j/94917 916635?pwd=NWplK0FjZHNldVRXSmcxSnFwdVg0QT09\n\nMeeting ID: 949 1791 6635\n Password: 085148\n LOCATION:https://researchseminars.org/talk/RJWAPDE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Tatiana Toro (U. Washington) DTSTART:20200514T180000Z DTEND:20200514T190000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/4 DESCRIPTION:Title: Elliptic measure and the geometry of domains in Euclidean space\nby Ta tiana Toro (U. Washington) as part of Rio de Janeiro webinar on analysis a nd partial differential equations\n\n\nAbstract\nIn this talk we will disc uss the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. In particular we will examine the relationship between the behavior of the elliptic measure of a certain class divergence form uniformly elliptic operators on a domain a nd the structure of its boundary. This work mixes elements of geometric me asure theory\, free boundary regularity problems and harmonic analysis.\n\ nTo join Prof. Tatiana's talk\, please use the following link and informat ion:\n\nhttps://puc-rio.zoom.us/j/402375411?pwd=N05uYWVBOGMzRm4yU21kSjBjYV RVUT09\n\nMeeting ID: 402 375 411\nPassword: 084011\n LOCATION:https://researchseminars.org/talk/RJWAPDE/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Giuseppe Mingione (University of Parma) DTSTART:20200507T140000Z DTEND:20200507T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/5 DESCRIPTION:Title: Gradient estimates\nby Giuseppe Mingione (University of Parma) as part of Rio de Janeiro webinar on analysis and partial differential equations\ n\n\nAbstract\nI am going to give a review of gradient estimates for solut ions to nonlinear elliptic and parabolic equations\, with special emphasis on Nonlinear Potential Theory. Non-uniformly elliptic problems will also be treated.\n\nTo access the seminar\, please use the following informatio n:\n\nhttps://zoom.us/j/96230784442?pwd=Um9VVzdnTGpaVzNjeHNyd3oyR25VUT09\n \nMeeting ID: 962 3078 4442\nPassword: 045854\n LOCATION:https://researchseminars.org/talk/RJWAPDE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Susanna Terracini (U. Torino) DTSTART:20200521T150000Z DTEND:20200521T160000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/6 DESCRIPTION:Title: Segregation\, interaction of species and related free boundary problems.\nby Susanna Terracini (U. Torino) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstract\nPartial differe ntial equations are often used to describe physical laws governing a compl icated system in a confined space with relatively simpler behaviour on the boundary. Thus\, reaction-diffusion systems with strong interaction term s appear in many multi-species physical problems as well as in population dynamics\, chemistry and material science. The qualitative properties of t he solutions and their limiting profiles in different regimes will be cons idered\, as well as the interfaces.\n\nTo join Prof. Terracini's lecture\, please use the following information:\n\nhttps://puc-rio.zoom.us/j/995466 16886?pwd=NHcvM1BXZ3hqNmI5R0YybkFmZmE4QT09\n\nMeeting ID: 995 4661 6886\nP assword: 046379\n LOCATION:https://researchseminars.org/talk/RJWAPDE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Filomena Pacella (U. Roma\, Sapienza) DTSTART:20200528T130000Z DTEND:20200528T140000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/7 DESCRIPTION:Title: Critical exponents for a class of fully nonlinear equations\nby Filome na Pacella (U. Roma\, Sapienza) as part of Rio de Janeiro webinar on analy sis and partial differential equations\n\n\nAbstract\nWe consider a class of radial fully nonlinear equations involving the extremal Pucci's operato rs and power nonlinearities.\nFor such equations some critical exponents w ere introduced by P.Felmer and A.Quaas in 2003\, motivated by the study of positive entire radial solutions.\nIn the first part of the talk I will d iscuss the role and properties of such exponents and its relation with con centration phenomena and energy invariance.\nIn the second part I will pre sent an alternative proof of the existence and uniqueness of these critica l exponents\, entirely based on the study of an associated quadratic dynam ical system. This approach also allows to get in a unified and simple way new existence and classification results for singular solutions as well as to prove that the same critical exponents give a threshold for the existe nce or nonexistence of positive radial solutions for the Dirichlet problem in exterior domains. This last result was recently proved by G.Galise\, A.Iacopetti and F. Leoni (2019) with a different proof.\nThe results prese nted are contained in several joint papers with I.Birindelli\, G.Galise\, F.Leoni\, L.Maia\, G.Saller Nornberg.\n\nTo join Prof. Pacella's talk\, pl ease use the following information.\n\nLink to join the talk:\nhttps://puc -rio.zoom.us/j/91799849377?pwd=bjU4MkpMdC9sWit3bGJQNTBQcnY3UT09\n\nMeeting ID: 917 9984 9377\nPassword: 801822\n LOCATION:https://researchseminars.org/talk/RJWAPDE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariana Smit Vega Garcia (Western Washington University) DTSTART:20200612T170000Z DTEND:20200612T180000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/8 DESCRIPTION:Title: Regularity of almost minimizers with free boundary\nby Mariana Smit Ve ga Garcia (Western Washington University) as part of Rio de Janeiro webina r on analysis and partial differential equations\n\n\nAbstract\nWe study a lmost minimizer for functionals which yield a free boundary\, as in the wo rk of Alt-Caffarelli and Alt-Caffarelli-Friedman. The almost minimizing pr operty can be understood as the defining characteristic of a minimizer in a problem which explicitly takes noise into account. In this talk\, we dis cuss the regularity of almost minimizers to energy functionals with variab le coefficients. This is joint work with Guy David\, Max Engelstein & Tati ana Toro.\n\nTo join Mariana's webinar\, please use the following informat ion:\n\nLink to joni Mariana's talk:\nhttps://puc-rio.zoom.us/j/9477258770 2?pwd=MHFJWjRFZ244eXYrN0ZkWFNRMElpZz09\n\nMeeting ID: 947 7258 7702\nPassw ord: 261257\n LOCATION:https://researchseminars.org/talk/RJWAPDE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Tavares (Instituto Superior Técnico\, IST-Lisbon) DTSTART:20200618T150000Z DTEND:20200618T160000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/9 DESCRIPTION:Title: Behavior near criticality of sign-changing solutions to the Lane-Emden equ ation with Dirichlet and Neumann boundary conditions\nby Hugo Tavares (Instituto Superior Técnico\, IST-Lisbon) as part of Rio de Janeiro webin ar on analysis and partial differential equations\n\n\nAbstract\nIn this t alk we will be concerned with several recent results on the classical Lane -Emden equation in a bounded domain\, with either Dirichlet or Neumann bou ndary conditions.\nIn the first part of the talk\, for radial solutions an d in the case of the ball in dimension 3 or higher\, we provide sharp rate s and constants describing the asymptotic behavior (as we approach the Sob olev critical exponent) of all local minima and maxima of the solutions\, as well as its derivative at roots. As corollaries\, we complement a known asymptotic approximation of the Dirichlet nodal solution in terms of a to wer of bubbles and present a similar formula for the Neumann problem.\nIn the second part or the talk we analyse the nonradial case with Neumann bou ndary conditions\, namely the existence (and symmetry) of least energy sol utions and their dependence on the exponent of the nonlinearity up to the Sobolev critical exponent\, discussing also the slightly supercritical cas e.\nThe talk is based on joint works with Alberto Saldaña\, Angela Pistoi a and Massimo Grossi.\n\nTo join Hugo's talk\, please use the following in formation:\n\nLink to join Hugo's talk:\nhttps://puc-rio.zoom.us/j/9641514 5570?pwd=TERzRmp1Z2RyU2x6OU92dFdHUnBmZz09\n\nMeeting ID: 964 1514 5570\nPa ssword: 125966\n LOCATION:https://researchseminars.org/talk/RJWAPDE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yehuda Pinchover (Technion) DTSTART:20200813T130000Z DTEND:20200813T140000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/10 DESCRIPTION:Title: How large can Hardy-weight be?\nby Yehuda Pinchover (Technion) as par t of Rio de Janeiro webinar on analysis and partial differential equations \n\n\nAbstract\nIn the first part of the talk we will discuss the existenc e of optimal Hardy-type inequalities with 'as large as possible' Hardy-wei ght for a general second-order elliptic operator defined on noncompact Rie mannian manifolds and discrete graphs\, while the second part of the talk will be devoted to a sharp answer to the question: "How large can Hardy-we ight be?"\n LOCATION:https://researchseminars.org/talk/RJWAPDE/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Noemi Wolanski (U. Buenos Aires) DTSTART:20200827T140000Z DTEND:20200827T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/11 DESCRIPTION:Title: Fractional heat equations with memory in $\\R^N$. Behavior in $L^p(\\R^N) $\nby Noemi Wolanski (U. Buenos Aires) as part of Rio de Janeiro webin ar on analysis and partial differential equations\n\n\nAbstract\nTo access the abstract of Prof. Noemi Wolanski's talk\, please\, use the following link:\n\nhttps://www.dropbox.com/s/zb8tan4j0fk1clm/abstract_wolanski.pdf?d l=0\n LOCATION:https://researchseminars.org/talk/RJWAPDE/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria J. Esteban (CEREMADE) DTSTART:20200917T130000Z DTEND:20200917T140000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/12 DESCRIPTION:Title: Magnetic interpolation inequalities\nby Maria J. Esteban (CEREMADE) a s part of Rio de Janeiro webinar on analysis and partial differential equa tions\n\n\nAbstract\nIn this talk I will present various results concernin g interpolation inequalities\, best constants and information about the ex tremal functions involving Schrödinger magnetic operators in dimensions 1 \, 2 and 3. The particular\, and physical interesting\, cases of constant and of Aharonov-Bohm magnetic fields will be discussed in detail.\n\nThese works have been made in collaboration with D. Bonheure\, J. Dolbeault\, A . Laptev and M. Loss.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Allen (Brigham Young U.) DTSTART:20200924T160000Z DTEND:20200924T170000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/13 DESCRIPTION:Title: A boundary Harnack principle for equations with nonzero right hand side\nby Mark Allen (Brigham Young U.) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstract\nThe boundary Ha rnack principle allows one to compare the behavior of two harmonic solutio ns when they both vanish on the boundary. This principle has proven useful in PDE\, harmonic analysis\, and free boundary problems. In this talk I w ill review the principle and some of its applications. I will then introdu ce a new boundary Harnack principle for functions whose Laplacian has nonz ero right hand sides. This new principle has applications to Hele-Shaw flo w as well as free boundary problems. I will also show how we have recently proven this result for fully nonlinear equations as well as the p-Laplaci an. This is joint work with Dennis Kriventsov and Henrik Shahgholian.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Maggi (UT Austin) DTSTART:20201009T160000Z DTEND:20201009T170000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/14 DESCRIPTION:Title: Symmetry of Plateau Surfaces and the Moving Planes Method with Singularit ies\nby Francesco Maggi (UT Austin) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstract\nBy employing the method of moving planes in a novel way we extend some classical symme try and rigidity results for smooth minimal surfaces to surfaces that have singularities of the sort typically observed in soap films. This is a joi nt work with Jacob Bernstein at Johns Hopkins University.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Porretta (Roma Tor Vergata) DTSTART:20201016T130000Z DTEND:20201016T140000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/16 DESCRIPTION:Title: Mean field games: a bridge between Hamilton-Jacobi and transport-diffusio n equations\nby Alessio Porretta (Roma Tor Vergata) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstra ct\nMean field game theory was developed since 2006 by J.‑M. Lasry and P .‑L. Lions in order to adapt the concept of Nash equilibria to different ial games with infinitely many players. In this context\, the value functi on of any small player depends on the distribution law of the dynamical st ate of the system. This model leads to systems of PDEs coupling Hamilton –Jacobi with Fokker–Planck (or continuity) equations. In this talk I w ill describe some features of mean field game systems and their connection with optimal control and optimal transport\, pointing out the role played by weak solutions\, renormalized formulations\, convex analysis and adjoi nt methods.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Héctor Chang-Lara (CIMAT) DTSTART:20201113T160000Z DTEND:20201113T170000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/17 DESCRIPTION:Title: Eikonal vs. Brownian: Regularity for the solution of an equation with gra dient constraint.\nby Héctor Chang-Lara (CIMAT) as part of Rio de Jan eiro webinar on analysis and partial differential equations\n\n\nAbstract\ nTwo controllers are in charge of steering a spaceship in some domain Omeg a. The first controller wants to spend as much time as possible exploring Omega while the second wants to get out of it as quickly as possible. The first controller determines minute by minute whether the ship is moving by a Brownian motion or with constant speed\, in which case it is the second controller who chooses the direction. Under these instructions\, determin ing the optimal strategies for each player leads us to solve the equation $\\min (-\\Delta u\, |Du|) = 1$ which has several interesting characterist ics. Among them is the presence of a free boundary which separates the reg ions where a Poisson or an Eikonal equation is satisfied. In a recent coll aboration with Edgard Pimentel (PUC-Rio) we showed that the solutions are Lipschitz continuous and that $|Du|$ is continuous\, even though the gradi ent is discontinuous in numerous examples. This problem is a simplificatio n of interesting models in financial mathematics related with the optimal strategy for the payment of dividends from multiple insurances.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Edriss S. Titi (U. Cambridge\, Texas A&M U. and Weizmann Institute of Science) DTSTART:20201127T140000Z DTEND:20201127T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/18 DESCRIPTION:Title: Recent Advances Concerning the Navier-Stokes and Euler Equations\nby Edriss S. Titi (U. Cambridge\, Texas A&M U. and Weizmann Institute of Scie nce) as part of Rio de Janeiro webinar on analysis and partial differentia l equations\n\n\nAbstract\nIn this talk I will discuss some recent progres s concerning the Navier-Stokes and Euler equations of incompressible fluid . In particular\, issues concerning the lack of uniqueness using the conve x integration machinery and their physical relevance. Moreover\, I will sh ow the universality of the critical $1/3$ H\\"older exponent\, conjectured by Onsager for the preservation of energy in Euler equations\, by extendi ng the Onsager conjecture for the preservation of generalized entropy in g eneral conservation laws. In addition\, I will present a blow-up criterio n for the 3D Euler equations based on a class of inviscid regularization f or these equations and the effect of physical boundaries on the potential formation of singularity.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/18/ END:VEVENT BEGIN:VEVENT SUMMARY:YanYan Li (Rutgers U.) DTSTART:20201203T150000Z DTEND:20201203T160000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/19 DESCRIPTION:Title: Gradient estimates for the insulated conductivity problem\nby YanYan Li (Rutgers U.) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstract\nIn this talk\, we discuss the insula ted conductivity problem with multiple inclusions embedded in a bounded do main in $n$-dimensional Euclidean space. The gradient of a solution may bl ow up as two inclusions approach each other. The optimal blow up rate was known in dimension $n=2$. It was not known whether the established upper b ound of the blow up rates in higher dimensions were optimal. We answer thi s question by improving the previously known upper bound of the blow up r ates in dimension $n>2$. This is a joint work with Zhuolun Yang.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Fonseca (Carnegie Mellon University) DTSTART:20210305T150000Z DTEND:20210305T160000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/20 DESCRIPTION:Title: Phase Transitions in Heterogeneous Media: Equilibria and Geometric Flows< /a>\nby Irene Fonseca (Carnegie Mellon University) as part of Rio de Janei ro webinar on analysis and partial differential equations\n\n\nAbstract\nA variational model in the context of the gradient theory for fluid-fluid p hase transitions with small scale heterogeneities is studied. In the case where the scale of the small homogeneities is of the same order of the sca le governing the phase transition\, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial ene rgy.\n\nThe underlying gradient flow provides unconditional convergence re sults for an Allen-Cahn type bi-stable reaction diffusion equation in a pe riodic medium. The limiting dynamics are given by an analog for anisotropi c mean curvature flow\, of the formulation due to Ken Brakke. As an essent ial ingredient in the analysis\, an explicit expression for the effective surface tension\, which dictates the limiting anisotropic mean curvature\, is obtained.\n\nThis is joint work with Riccardo Cristoferi (Radboud Univ ersity\, The Netherlands)\, Adrian Hagerty\, Cristina Popovici\, Rustum Ch oksi (McGill)\, Jessica Lin (McGill)\, and Raghavendra Venkatraman (CMU).\ n LOCATION:https://researchseminars.org/talk/RJWAPDE/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Herbert Koch (Mathematisches Institut\, U. Bonn) DTSTART:20210318T140000Z DTEND:20210318T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/21 DESCRIPTION:Title: Sobolev regularity for the infinity Laplace equation\nby Herbert Koch (Mathematisches Institut\, U. Bonn) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstract\nThe infinity La place equation is a very degenerate elliptic equation. I report on Sobolev regularity of $|Du|^a$\, both for solutions to the homogeneous and the in homogeneous equation in 2d. This is joint work with Yi Ru-Ya Zhang and Yua n Zhou.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvia Serfaty (CIMS\, NYU) DTSTART:20210409T140000Z DTEND:20210409T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/22 DESCRIPTION:Title: Mean-Field limits of Coulomb-type dynamics\nby Sylvia Serfaty (CIMS\, NYU) as part of Rio de Janeiro webinar on analysis and partial differenti al equations\n\n\nAbstract\nWe consider a system of $N$ particles evolving according to the gradient flow of their Coulomb or Riesz interaction\, or a similar conservative flow\, and possible added random diffusion. By Rie sz interaction\, we mean inverse power $s$ of the distance. We present a c onvergence result as $N$ tends to infinity to the expected limiting mean f ield evolution equation. We also discuss the derivation of Vlasov-Poisson from newtonian dynamics in the monokinetic case\, as well as related resul ts for Ginzburg-Landau vortex dynamics.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabrielle S. Nornberg (Universidade de São Paulo (ICMC-USP)) DTSTART:20210507T140000Z DTEND:20210507T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/23 DESCRIPTION:Title: Qualitative properties of Lane-Emden type systems\nby Gabrielle S. No rnberg (Universidade de São Paulo (ICMC-USP)) as part of Rio de Janeiro w ebinar on analysis and partial differential equations\n\n\nAbstract\nIn th is talk we discuss some qualitative properties of Lane-Emden type systems and their applications to existence and nonexistence of solutions.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrzej Święch (Georgia Institute of Technology) DTSTART:20210422T140000Z DTEND:20210422T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/24 DESCRIPTION:Title: Singular perturbations and optimal control of stochastic systems in infin ite dimension\nby Andrzej Święch (Georgia Institute of Technology) a s part of Rio de Janeiro webinar on analysis and partial differential equa tions\n\n\nAbstract\nWe will discuss a stochastic optimal control problem for a two scale system driven by an infinite dimensional stochastic differ ential equation which consists of ''slow'' and ''fast'' components. We wil l consider a rather general case where the evolution is given by an abstra ct semilinear stochastic differential equation with nonlinear dependence o n the controls. We will present a PDE approach to the problem based on the theory of viscosity solutions in Hilbert spaces. This approach allows to prove that as the speed of the fast component goes to infinity\, the value functions of the optimal control problems converge to the viscosity solut ion of a reduced effective equation. Our results generalize to the infinit e dimensional case the finite dimensional results of Alvarez and Bardi and complement recent results in Hilbert spaces obtained by Guatteri and Tess itore.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabella Ianni (Sapienza Università di Roma) DTSTART:20210521T140000Z DTEND:20210521T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/25 DESCRIPTION:Title: Radial and non-radial solutions for the Lane-Emden problem in the disk\nby Isabella Ianni (Sapienza Università di Roma) as part of Rio de Jane iro webinar on analysis and partial differential equations\n\n\nAbstract\n We discuss sharp asymptotic analysis results on radial solutions of the La ne-Emden problem in the disk\, which in particular lead to a Morse index f ormula. \nAs a consequence we can prove the existence of new unexpected so lutions. The talk is based on results mainly contained in [ADI]\, [IS]\, [ GI] and [DIP].\n\n[ADI] A. Amadori\, F. De Marchis\, I. Ianni\, Morse inde x computation for radial solutions of the Henon problem in the disk\, prep rint\n\n[IS] I. Ianni\, A. Saldana\, Sharp asymptotic behavior of radial s olutions of some planar semilinear elliptic problems\, preprint\n\n[GI] I. Ianni\, F. Gladiali\, Quasi-radial solutions for the Lane-Emden problem i n the ball\, NoDEA 27 (2) (2020)\n\n[DIP] F. De Marchis\, I. Ianni\, F. Pa cella\, Exact Morse index computation for nodal radial solutions of Lane-E mden problems\, Mathematische Annalen 367 (2017)\n LOCATION:https://researchseminars.org/talk/RJWAPDE/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Diego R. Moreira (Universidade Federal do Ceará) DTSTART:20210618T140000Z DTEND:20210618T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/26 DESCRIPTION:Title: Up to the boundary gradient estimates for solutions to nonlinear free bou ndary problems with unbounded measurable ingredients\nby Diego R. More ira (Universidade Federal do Ceará) as part of Rio de Janeiro webinar on analysis and partial differential equations\n\n\nAbstract\nIn this talk\, we discuss recent advances on up to the boundary gradient estimates for vi scosity solutions of free boundary problems governed by fully nonlinear an d quasilinear equations with unbounded coefficients. We present the new In homogeneous Pucci Barriers as new elements for the proof. If time permits \, we discuss some of the main steps in the proof\, namely\, the trace es timate of the solution on the points of the fixed boundary that projects n ontangentially over the free boundary. These methods are inspired by some ideas of Carlos Kenig in Harmonic Analysis.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Yannick Sire (Johns Hopkins U.) DTSTART:20210715T140000Z DTEND:20210715T150000Z DTSTAMP:20260422T212902Z UID:RJWAPDE/27 DESCRIPTION:Title: Blow-up solutions via parabolic gluing\nby Yannick Sire (Johns Hopkin s U.) as part of Rio de Janeiro webinar on analysis and partial differenti al equations\n\n\nAbstract\nWe will present some recent results on the con struction of blow-up solutions for critical parabolic problems of geometri c flavor. Initiated in the recent years\, the inner/outer parabolic gluing is a very versatile parabolic version of the well-known Lyapunov-Schmidt reduction in elliptic PDE theory. The method allows to prove rigorously so me formal matching asymptotics (if any available) for several PDEs arising in porous media\, geometric flows\, etc….I will give an overview of the strategy and will present several applications to (variations of) the har monic map flow\, Yamabe flow and Yang-Mills flow. I will also present some open questions.\n LOCATION:https://researchseminars.org/talk/RJWAPDE/27/ END:VEVENT END:VCALENDAR