Gradient estimates for nonlinear kinetic Fokker-Planck equations

Fuente: arXiv
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Main Authors: Kim, Kyeongbae, Lee, Ho-Sik, Nowak, Simon
Format: Preprint
Published: 2025
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author Kim, Kyeongbae
Lee, Ho-Sik
Nowak, Simon
author_facet Kim, Kyeongbae
Lee, Ho-Sik
Nowak, Simon
contents In this work, we provide a comprehensive gradient regularity theory for a broad class of nonlinear kinetic Fokker-Planck equations. We achieve this by establishing precise pointwise estimates in terms of the data in the spirit of nonlinear potential theory, leading to fine gradient regularity results under borderline assumptions on the data. Notably, our gradient estimates are novel already in the absence of forcing terms and even for linear kinetic Fokker-Planck equations in divergence form.
format Preprint
id arxiv_https___arxiv_org_abs_2502_09366
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gradient estimates for nonlinear kinetic Fokker-Planck equations
Kim, Kyeongbae
Lee, Ho-Sik
Nowak, Simon
Analysis of PDEs
In this work, we provide a comprehensive gradient regularity theory for a broad class of nonlinear kinetic Fokker-Planck equations. We achieve this by establishing precise pointwise estimates in terms of the data in the spirit of nonlinear potential theory, leading to fine gradient regularity results under borderline assumptions on the data. Notably, our gradient estimates are novel already in the absence of forcing terms and even for linear kinetic Fokker-Planck equations in divergence form.
title Gradient estimates for nonlinear kinetic Fokker-Planck equations
topic Analysis of PDEs
url https://arxiv.org/abs/2502.09366