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arXiv · 2410.15782

Boundary estimates for non-divergence equations in $C^1$ domains

Clara Torres-Latorre
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Abstract

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.

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Clara Torres-Latorre. 2024-10-21. Boundary estimates for non-divergence equations in $C^1$ domains. https://arxiv.org/abs/2410.15782

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