Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations

Abstract: We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving an interpolative apriori boundedness estimate for weak subsolutions in terms of a tail term encoding the nonlocal contributions of the diffusion.