English

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

Analysis of PDEs 2025-12-29 v4

Abstract

We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence equations in C1C^1 domains, providing an explicit modulus 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 flat Lipschitz domains, unifying both theories with a single proof.

Keywords

Cite

@article{arxiv.2410.15782,
  title  = {Boundary estimates for non-divergence equations in $C^1$ domains},
  author = {Clara Torres-Latorre},
  journal= {arXiv preprint arXiv:2410.15782},
  year   = {2025}
}

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22 pages