New preprint about the Boltzmann equation

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

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

Mostly Maximum principle

Mostly Maximum principle

This conference is organised by I. Birindelli, I. Capuzzo Dolcetta, F. Leoni, M. Transirico and A. Vitolo. It will take place in September 16 – 18, at Agropoli, one hour of train in the south of Napoli.

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