Hölder Regularity for Hypoelliptic Kinetic Equations with Rough Diffusion Coefficients

François Golse (1) , Alexis F. Vasseur (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Department of Mathematics

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 Hölder regularity version of the classical averaging lemmas.

Mots clés: Hypoellipticity; Kinetic equations; Regularity; Fokker-Planck equation; DeGiorgi method

Domaines: Equations aux dérivées partielles [math.AP]

François Golse, Alexis F. Vasseur. Hölder Regularity for Hypoelliptic Kinetic Equations with Rough Diffusion Coefficients. 2015. ⟨hal-01160566v1⟩