On the De Giorgi-Nash-Moser weak regularity theory for kinetic operators

The aim of this talk is to discuss the most recent developments of the De Giorgi-Nash-Moser weak regularity theory for kinetic operators. The analysis will be presented in the model case of the Fokker-Planck equation with measurable coefficients in divergence form and the focus will be on exploring qualitative and quantitative methods to prove an invariant Harnack inequality for non-negative solutions. Finally, some applications of this inequality to various kinetic models will be discussed.