English

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

R2 v1 2026-06-22T09:47:57.260Z