Boundary estimates for non-divergence equations in $C^1$ domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914220892749824 |
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| author | Torres-Latorre, Clara |
| author_facet | Torres-Latorre, Clara |
| contents | We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence equations in $C^1$ domains, providing an explicit modulus of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with $C^{1,\mathrm{Dini}}$ boundaries, while also recovering the known $C^{1-\varepsilon}$ regularity for flat Lipschitz domains, unifying both theories with a single proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary estimates for non-divergence equations in $C^1$ domains Torres-Latorre, Clara Analysis of PDEs 35B65, 35J25 We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence equations in $C^1$ domains, providing an explicit modulus of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with $C^{1,\mathrm{Dini}}$ boundaries, while also recovering the known $C^{1-\varepsilon}$ regularity for flat Lipschitz domains, unifying both theories with a single proof. |
| title | Boundary estimates for non-divergence equations in $C^1$ domains |
| topic | Analysis of PDEs 35B65, 35J25 |
| url | https://arxiv.org/abs/2410.15782 |