arXiv:2410.15782 Abstract | arXiv Analytics

arXiv:2410.15782 [math.AP]Abstract References Reviews Resources

Boundary estimates for harmonic functions in $C^1$ domains

Published 2024-10-21Version 1

We obtain boundary nondegeneracy and regularity estimates for harmonic functions 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.

Comments: 26 pages

Categories: math.AP

Subjects: 31B25, 35B65, 35J25

Keywords: harmonic functions, boundary estimates, boundary lipschitz regularity, flat lipschitz domains, results extend

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