Modeling, analysis, computation and application of kinetic equations

Holder regularity for hypoelliptic kinetic equations with rough diffusion coefficients

Alexis Vasseur

University of Texas at Austin

In this talk, we will present an 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 Holder regularity version of the classical averaging lemmas.