Gradient estimates for nonlinear kinetic Fokker-Planck equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912231291092992 |
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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 |