Kinetic maximal [formula omitted]-regularity for the fractional Kolmogorov equation with variable density

Abstract

We consider the Kolmogorov equation, where the right-hand side is given by a non-local integro-differential operator comparable to the fractional Laplacian in velocity with possibly time, space and velocity dependent density. We prove that this equation admits kinetic maximal Lμp-regularity under suitable assumptions on the density and on p and μ. We apply this result to prove short-time existence of strong Lμp-solutions to quasilinear non-local kinetic partial differential equations.