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arXiv · 1912.11958

Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations

Yuanyuan Lian·Wenxiu Xu·Kai Zhang
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Abstract

In this paper, we prove the boundary Lipschitz regularity and the Hopf Lemma by a unified method on Reifenberg domains for fully nonlinear elliptic equations. Precisely, if the domain $\Omega$ satisfies the exterior Reifenberg $C^{1,\mathrm{Dini}}$ condition at $x_0\in \partial \Omega$ (see Definition 1.3), the solution is Lipschitz continuous at $x_0$; if $\Omega$ satisfies the interior Reifenberg $C^{1,\mathrm{Dini}}$ condition at $x_0$ (see Definition 1.4), the Hopf lemma holds at $x_0$. Our paper extends the results under the usual $C^{1,\mathrm{Dini}}$ condition.

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Yuanyuan Lian, Wenxiu Xu, Kai Zhang. 2019-12-27. Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations. https://arxiv.org/abs/1912.11958

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