Existence and non-existence of minimizers for a Poincaré-Sobolev inequality.

Date/heure
28 novembre 2019
14:15 - 15:15

Oratrice ou orateur
Hanne van den Bosch

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse


Résumé

We study a specific Poincaré-Sobolev inequality in bounded domains, that has recently been used to prove a semi-classical bound on the kinetic energy of fermionic many-body states. The corresponding inequality in the entire space is precisely scale invariant and this gives rise to an interesting phenomenon. Optimizers exist for some (most ?) domains and do not exist for some other domains, at least for the isosceles triangle in two dimensions. In this talk, I will discuss bounds on the constant in the inequality and the proofs of existence and non-existence. This is joint work with Rafael Benguria and Cristà³bal Vallejos (PUC, Chile).