A new preprint entitled « The Schauder estimate for kinetic integral equations » is available on arxiv and hal. This is a joint work with Luis Silvestre. Abstract: We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form ft+v⋅∇xf=Lvf+c, where Lv is an integro-differential diffusion operator of order 2s acting … Lire la suite

# Filed under Prépublication …

## New preprint: Decay estimates for large velocities in the Boltzmann equation without cut-off

C. Mouhot, L. Silvestre and myself just uploaded on HAL and arXiv a new preprint entitled Decay estimates for large velocities in the Boltzmann equation without cut-off. Abstract: We establish pointwise large velocity decay rates for the solution of the inhomogeneous Boltzmann equation without cutoff, under the assumption that three hydrodynamic quantities (mass, energy, entropy … Lire la suite

## New preprint: A toy model in kinetic theory

I just uploaded on HAL and arxiv a new preprint entitled « A nonlinear toy model from kinetic theory », in collaboration with C. Mouhot (Cambridge). Abstract: This note is concerned with the study of a toy nonlinear model in kinetic theory. It consists in a non-linear kinetic Fokker-Planck equation whose diffusion in the velocity variable is … Lire la suite

## New preprint: flux-limited solutions & classical viscosity solutions

We uploaded on hal with Guy Barles, Ariela Briani and Emmanuel Chasseigne a preprint entitled Flux-limited and classical viscosity solutions for regional control problems. Abstract: The aim of this paper is to compare two different approaches for regional control problems: the first one is the classical approach, using a standard notion of viscosity solutions, which … Lire la suite

## New preprint about singular/degenerate parabolic equations

With Tianling Jin and Luis Silvestre, we uploaded on arxiv and hal a preprint entitled Hölder gradient estimates for a class of singular or degenerate parabolic equations. Abstract: We prove interior Hölder estimate for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic equation ut=|∇u|κdiv(|∇u|{p−2}∇u), where p∈(1,∞) and κ∈(1−p,∞). This includes … Lire la suite

## New preprint about the Boltzmann equation

We wrote with Luis Silvestre a paper entitled « Weak Harnack inequality for the Boltzmann equation without cut-off ». See arxiv and hal. Abstract: « In this paper, we obtain the weak Harnack inequality and H\ »older estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can be written in this … Lire la suite

## New preprint about kinetic Fokker-Planck equations

I recently uploaded a new preprint on HAL and arxiv entitled « Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation ». It is written in collaboration with François Golse, Clément Mouhot and Alexis F. Vasseur. Abstract: We extend the De~Giorgi–Nash–Moser theory to a class of kinetic Fokker-Planck equations and deduce … Lire la suite

## Final version of the paper about HJ equations on networks

I uploaded on HAL and arxiv the revised and final version (we hope so! it is the fifth one) of the paper we wrote with Régis Monneau about Hamilton-Jacobi equations on networks. This new version contains new results concerning flux-limited subsolutions. Indeed, Jessica Guerand pointed out to us a mistake in the proof where it … Lire la suite

## New preprint: Global Well-posedness of a Nonlocal Burgers equation: the periodic case

A new preprint on HAL and arxiv written with Roman Shvydkoy and François Vigneron. Abstract: This paper is concerned with the study of a non-local Burgers equation for positive bounded periodic initial data. The equation reads u_t – u |D| u + |D|(u^2) = 0. We construct global classical solutions starting from smooth positive data, … Lire la suite

## New preprint: Hölder continuity of solutions to quasilinear hypoelliptic equations

I just uploaded on HAL and arXiv a new preprint entitled « Hölder continuity of solutions to quasilinear hypoelliptic equations » written with Clément Mouhot. Abstract: We prove that L2 weak solutions to a quasilinear hypoelliptic equations with bounded measurable coefficients are Hölder continuous. The proof relies on classical techniques developed by De Giorgi and Moser together … Lire la suite