Global Hölder Solvability of parabolic equations on domains with capacity density conditions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911356500836352 |
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| author | Hara, Takanobu |
| author_facet | Hara, Takanobu |
| contents | We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally Hölder continuous solutions. Notably, our results accommodate data exhibiting singularities nearly as critical as the inverse square of the distance from the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Hölder Solvability of parabolic equations on domains with capacity density conditions Hara, Takanobu Analysis of PDEs Primary: 35K20, Secondary: 35B65, 35R05, 31B15 We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally Hölder continuous solutions. Notably, our results accommodate data exhibiting singularities nearly as critical as the inverse square of the distance from the boundary. |
| title | Global Hölder Solvability of parabolic equations on domains with capacity density conditions |
| topic | Analysis of PDEs Primary: 35K20, Secondary: 35B65, 35R05, 31B15 |
| url | https://arxiv.org/abs/2601.02863 |