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Nikita Simonov - Stability in Gagliardo-Nirenberg-Sobolev inequalities

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FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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