Séminaire EDP-Analyse ICJ

Stability in Gagliardo-Nirenberg-Sobolev inequalities

by Nikita Simonov (LaMMe, Université d'Évry Val d'Essonne)

Europe/Paris
Fokko (ICJ)

Fokko

ICJ

Description

In some functional inequalities, best constants and minimizers are known. The next question is stability: suppose that a function "almost attains the equality", in which sense it is close to one of the minimizers? In this lecture, I will address a recent result on the quantitative stability of a subfamily of Gagliardo-Nirengerg-Sobolev inequalities. The approach is based on the entropy method for the fast diffusion equation and allows us to obtain completely constructive estimates. The results are based on joint work with M. Bonforte, J. Dolbeault, and B. Nazaret.