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

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.

arXiv commentarXiv admin note: text overlap with arXiv:1812.11357

References in corpus (1)

• Boundary estimates for positive solutions to second order elliptic equations