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arXiv · 2209.00769

Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations

Hongjie Dong·Timur Yastrzhembskiy
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Abstract

We present global Schauder type estimates in all variables and unique solvability results in kinetic H\"older spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading coefficients are H\"older continuous in the $x, v$ variables and are merely measurable in the temporal variable. Our proof is inspired by Campanato's approach to Schauder estimates and does not rely on the estimates of the fundamental solution of the KFP operator.

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Hongjie Dong, Timur Yastrzhembskiy. 2022-09-02. Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations. https://arxiv.org/abs/2209.00769

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