3 papers
math.AP2025
Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Francesca Anceschi, Helge Dietert, Jessica Guerand +5
We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörm…
math.AP2024
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…
math.AP2024
Regularity and trend to equilibrium for a non-local advection-diffusion model of active particles
Luca Alasio, Jessica Guerand, Simon Schulz
We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this eq…