New preprint about singular/degenerate parabolic equations

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

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