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arXiv · 2604.04819

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

Pêdra D. S. Andrade·Clara Torres-Latorre
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Abstract

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.

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Pêdra D. S. Andrade, Clara Torres-Latorre. 2026-04-06. Boundary estimates for parabolic non-divergence equations in $C^1$ domains. https://arxiv.org/abs/2604.04819

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