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 domains, providing explicit moduli of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with boundaries, while also recovering the known 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}
}
Comments
29 pages