Wednesday, May 26, 2021 — 5:00 pm — online talk

Quantitative De Giorgi method for kinetic Fokker-Planck equation

Abstract: (Joint work with Clément Mouhot) Our main motivation is to get quantitative regularity results for the Landau equation. As for elliptic and parabolic equations with rough coefficients, De Giorgi method allows to prove Hölder continuity and Harnack inequalities for kinetic equations. The idea here is to see the Landau equation as a linear kinetic Fokker-Planck one with rough coefficients. However, the De Giorgi method was known not to be quantitative for the Fokker-Planck equation because of one non quantitative step: the intermediate value lemma. Here we get a new quantitative intermediate lemma and we simplify some existing steps of the method in order to get a short self-contained quantitative proof for the Hölder continuity and Harnack inequalities for the kinetic Fokker-Planck equation.