Kinetic maximal Lμp(Lp)-regularity for the fractional Kolmogorov equation with variable density. (January 2022) - Niebel, Lukas
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 L μ p -regularity under suitable assumptions on the density and on p and μ . We apply this result to prove short-time existence of strong L μ p -solutions to quasilinear non-local kinetic partial differential equations.