Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Description
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Francesco Maggi - Univ. Texas Austin,
Titre Rigidity theorems for critical trace Sobolev inequality
Date27/06/2024
Horaire10:30 à 12:00
Diffusion
Résume

 For $n\ge 2$ and $p\in(1,n)$ the "best $p$-Sobolev inequality" on an open set $\Om\subset\R^n$ is identified with a family $\Phi_\Om$ of variational problems with critical volume and trace constraints. In joint work with Neumayer and Tomasetti we prove that, if $\Om$ is bounded, then (i) for every $n$ and $p$, there exist generalized minimizers of $\Phi_\Om$, having at most one boundary concentration point, and: (ii) if $n> 2\,p$, then there exist (classical) minimizers. We then establish rigidity results for the comparison theorem "balls have the worst best Sobolev inequalities", thus giving the first affirmative answers to a question raised in joint work with Villani (JGA 2005). A key ingredient in our analysis is the complete characterization of $\Phi_{Half Space}$ obtained in joint work with Neumayer (JFA 2017). Connections with the Yamabe problem are also discussed.

 

Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie
© IMJ-PRG