4 papers
Gehring's Lemma for kinetic Fokker-Planck equations
Jessica Guerand, Cyril Imbert, Clément Mouhot
In this article, we establish a "Gehring lemma" for a real function satisfying a reverse Hölder inequality on all "kinetic cylinders" contained in a large one: it asserts that the…
Global smooth solutions for triangular reaction-cross diffusion systems
Jessica Guerand, Angeliki Menegaki, Ariane Trescases
For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smo…
Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations
Jessica Guerand, Cyril Imbert
This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering…
Quantitative regularity for parabolic De Giorgi classes
Jessica Guerand
We deal with the De Giorgi H{ö}lder regularity theory for parabolic equations with rough coefficients and parabolic De Giorgi classes which extend the notion of solution. We give a…