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<p>We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence equations in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(C^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> domains, providing an explicit modulus of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(C^{1,\textrm{Dini}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mtext>Dini</mtext> </mrow> </msup> </math></EquationSource> </InlineEquation> boundaries, while also recovering the known <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(C^{1-\varepsilon }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>ε</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> regularity for flat Lipschitz domains, unifying both theories with a single proof.</p>

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Boundary estimates for non-divergence equations in \(C^1\) domains

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Clara Torres-Latorre

摘要

We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence equations in \(C^1\) C 1 domains, providing an explicit modulus of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with \(C^{1,\textrm{Dini}}\) C 1 , Dini boundaries, while also recovering the known \(C^{1-\varepsilon }\) C 1 - ε regularity for flat Lipschitz domains, unifying both theories with a single proof.