25/04/2026
L’information de Fisher, une des clés de l’équation de Boltzmann
La décroissance de l’information de Fisher sous l’effet des collisions et la régularité globale pour l’équation de Boltzmann.
Lire le billet22/01/2026
De Giorgi’s regularity for elliptic, parabolic and kinetic equations
Lecture notes based on talks given at Berkeley and devoted to a unified approach to regularity theory.
Read post05/01/2026
Kinetic program in Berkeley
An overview of the semester-long program Kinetic Theory: Novel Statistical, Stochastic and Analytical Methods, organized in Berkeley.
Read post05/01/2026
Chancellor’s courses
My appointment as Chancellor’s Visiting Professor and lectures on De Giorgi regularity.
Read post02/01/2026
Fisher for Boltzmann (review)
A presentation at the 2025 Journées EDP of a result on the monotonicity of the Fisher information.
Read post09/01/2025
Conditional decay for Boltzmann
A preprint with Amélie Loher on the appearance of velocity decay in a bounded domain.
Read post07/10/2024
Gehring’s lemma for kinetic equations
A kinetic extension of Gehring’s lemma and improved integrability for Fokker–Planck equations.
Read post04/09/2024
Fisher information for Boltzmann
With Luis Silvestre and Cédric Villani: the Fisher information decreases for a broad class of collision kernels.
Read post18/12/2023
Partial regularity for the Boltzmann equation
Partial regularity in time for very soft potentials; the set of singular times has controlled Hausdorff dimension.
Read post21/10/2023
Hamilton-Jacobi equations
Two preprints on Hamilton–Jacobi equations in domains: viscosity solutions, relaxation, and comparison principles.
Read post22/06/2022
Local regularity for the Landau equation
Joint work on local regularity for the Landau equation with very soft potentials.
Read post08/02/2021
Log-transform for kinetic FP equations
A weak Harnack inequality for kinetic Fokker–Planck equations obtained through a logarithmic transformation.
Read post22/06/2020
Regularity for the Boltzmann equation conditional to macroscopic bounds
A survey of a priori estimates and uniform regularity under control of mass, energy, and entropy.
Read post09/02/2020
Gaussian lower bounds for the Boltzmann equation
Gaussian lower bounds for the non-cutoff Boltzmann equation under hydrodynamic assumptions.
Read post09/02/2020
Global regularity estimates for the Boltzmann equation
A series of papers on a priori C∞ estimates for the inhomogeneous non-cutoff Boltzmann equation.
Read post07/02/2020
The Schauder estimate for kinetic integral equations
Interior Schauder estimates for kinetic equations with integro-differential diffusion.
Read post