On the De Giorgi-Nash-Moser regularity theory for kinetic equations

Abstract

In this note we review some recent results regarding the De Giorgi-Nash-Moser weak regularity theory for Kolmogorov operators obtained in [10] in collaboration with A. Rebucci. To simplify the treatment, we focus on the model case of the Fokker-Planck equation with rough coefficients and we highlight the main steps of the proof of a Harnack inequality for weak solutions.

Keywords

• kolmogorov-fokker-planck equation
• harnack inequality
• regularity theory