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arXiv · 2103.05966

Kinetic maximal $L^p_\mu(L^p)$-regularity for the fractional Kolmogorov equation with variable density

Lukas Niebel
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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 $L^p_\mu$-regularity under suitable assumptions on the density and on $p$ and $\mu$. We apply this result to prove short-time existence of strong $L^p_\mu$-solutions to quasilinear fractional kinetic partial differential equations.

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Lukas Niebel. 2021-03-10. Kinetic maximal $L^p_\mu(L^p)$-regularity for the fractional Kolmogorov equation with variable density. https://doi.org/10.1016/j.na.2021.112517

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