6 papers · 1 filter
De Giorgi's regularity theory for elliptic, parabolic and kinetic equations
Cyril Imbert
This book presents a comprehensive regularity theory for solutions of elliptic, parabolic, and kinetic equations. The foundation of this theory was laid by E. De Giorgi's groundbre…
Fisher information for solutions of the Boltzmann equation
Cyril Imbert
This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This cla…
Conditional appearance of decay for the non-cutoff Boltzmann equation in a bounded domain
Cyril Imbert, Amélie Loher
This work is concerned with the generation of decay estimates in the velocity variable for solutions of the space-inhomogeneous Boltzmann equation without cutoff on a bounded spati…
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…
On the monotonicity of the Fisher information for the Boltzmann equation
Cyril Imbert, Luis Silvestre, Cédric Villani
We prove that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all…
Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials
François Golse, Cyril Imbert, Luis Silvestre
We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials constructed as in Villani (1998) has Hausdorff dimension…