Abstract:
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. |