Boundary estimates for parabolic non-divergence equations in $C^1$ domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913007898984448 |
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| author | Andrade, Pêdra D. S. Torres-Latorre, Clara |
| author_facet | Andrade, Pêdra D. S. Torres-Latorre, Clara |
| contents | We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence form parabolic equations in parabolic $C^1$ domains, providing explicit moduli 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 parabolic Lipschitz domains, unifying both regimes with a single proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04819 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundary estimates for parabolic non-divergence equations in $C^1$ domains Andrade, Pêdra D. S. Torres-Latorre, Clara Analysis of PDEs 35B65, 35K20 We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence form parabolic equations in parabolic $C^1$ domains, providing explicit moduli 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 parabolic Lipschitz domains, unifying both regimes with a single proof. |
| title | Boundary estimates for parabolic non-divergence equations in $C^1$ domains |
| topic | Analysis of PDEs 35B65, 35K20 |
| url | https://arxiv.org/abs/2604.04819 |