BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hugo Tavares (Instituto Superior Técnico\, IST-Lisbon) DTSTART:20200618T150000Z DTEND:20200618T160000Z DTSTAMP:20260423T005813Z 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 END:VCALENDAR