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Kinetic maximal $L^p_μ(L^p)$-regularity for the fractional Kolmogorov equation with variable density (2103.05966v2)
Published 10 Mar 2021 in math.AP
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 $Lp_\mu$-regularity under suitable assumptions on the density and on $p$ and $\mu$. We apply this result to prove short-time existence of strong $Lp_\mu$-solutions to quasilinear fractional kinetic partial differential equations.