Stability in Gagliardo-Nirenberg-Sobolev inequalities (Nikita Simonov, Université Paris-Dauphine)

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 talk, 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 entirely constructive estimates. The results are based on joint work with M. Bonforte, J. Dolbeault, and B. Nazaret.