H\"{o}lder regularity for hypoelliptic kinetic equations with rough diffusion coefficients
Analysis of PDEs
2015-06-16 v2
Abstract
This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only in the velocity variable, while the Liouville transport operator has a mixing effect in the position/velocity phase space. The mixing effect is incorporated in the classical DeGiorgi method via the averaging lemmas. The result can be seen as a H\"{o}lder regularity version of the classical averaging lemmas.
Keywords
Cite
@article{arxiv.1506.01908,
title = {H\"{o}lder regularity for hypoelliptic kinetic equations with rough diffusion coefficients},
author = {François Golse and Alexis Vasseur},
journal= {arXiv preprint arXiv:1506.01908},
year = {2015}
}
Comments
21 pages. Statement of Lemma 3.2 corrected. Proof of Lemma 3.2 modified accordingly