A critical Poincaré-Sobolev inequality.



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 Cristóbal Vallejos (PUC, Chile).

Date: Apr 09, 2019 at 16:00:00 h
Venue: Sala de seminarios Felipe Álvarez, piso 5, DIM, U. de Chile. Beauchef 851, Torre Norte.
Speaker: Hanne Van Den Bosch
Affiliation: Depto. de Ingeniería Matemática, FCFM, U. de Chile.
Coordinator: Matteo Rizzi

Posted on Apr 2, 2019 in Differential Equations, Seminars