English

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

Analysis of PDEs 2026-04-07 v1

Abstract

We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence form parabolic equations in parabolic C1C^1 domains, providing explicit moduli of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with C1,DiniC^{1,\mathrm{Dini}} boundaries, while also recovering the known C1εC^{1-\varepsilon} regularity for parabolic Lipschitz domains, unifying both regimes with a single proof.

Keywords

Cite

@article{arxiv.2604.04819,
  title  = {Boundary estimates for parabolic non-divergence equations in $C^1$ domains},
  author = {Pêdra D. S. Andrade and Clara Torres-Latorre},
  journal= {arXiv preprint arXiv:2604.04819},
  year   = {2026}
}

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29 pages