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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.04121 |
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| _version_ | 1866918369757757440 |
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| author | Kim, Kyeongbae Weidner, Marvin |
| author_facet | Kim, Kyeongbae Weidner, Marvin |
| contents | We prove optimal regularity results for solutions to linear kinetic Fokker-Planck equations in bounded domains. Our contributions are two-fold. First, we establish the sharp $C^{1/2}$ regularity for either diffuse reflection or prescribed in-flow boundary conditions. Previously, in this setting, it was only known that solutions are $C^α$ for some small $α> 0$. Second, we provide a complete characterization of the solution behavior near the grazing set by proving higher order expansions beyond the critical regularity threshold of $\frac{1}{2}$. These results demonstrate for the first time that solutions maintain higher smoothness up to the grazing set near the incoming boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04121 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp regularity near the grazing set for kinetic Fokker-Planck equations Kim, Kyeongbae Weidner, Marvin Analysis of PDEs We prove optimal regularity results for solutions to linear kinetic Fokker-Planck equations in bounded domains. Our contributions are two-fold. First, we establish the sharp $C^{1/2}$ regularity for either diffuse reflection or prescribed in-flow boundary conditions. Previously, in this setting, it was only known that solutions are $C^α$ for some small $α> 0$. Second, we provide a complete characterization of the solution behavior near the grazing set by proving higher order expansions beyond the critical regularity threshold of $\frac{1}{2}$. These results demonstrate for the first time that solutions maintain higher smoothness up to the grazing set near the incoming boundary. |
| title | Sharp regularity near the grazing set for kinetic Fokker-Planck equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.04121 |