Yuanyuan Lian, Kai Zhang
Published 2018-12-29Version 1
In this note, we investigate the boundary H\"older regularity for fully nonlinear elliptic equations on Reifenberg flat domains. We will prove that for any $0<\alpha<1$, there exists $\delta>0$ such that the solutions are $C^{\alpha}$ at $x_0\in \partial \Omega$ provided that $\Omega$ is $(\delta,R)$-Reifenberg flat at $x_0$ (see Definition 1.1). A similar result for the Poisson equation has been proved by Lemenant and Sire [5], where the Alt-Caffarelli-Friedman's monotonicity formula is used. Besides the generalization to fully nonlinear elliptic equations, our method is simple. In addition, even for the Poisson equation, our result is stronger than that of Lemenant and Sire.
Regularity for fully nonlinear elliptic equations with oblique boundary conditions
Boundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations
Boundary Pointwise $C^{1,α}$ and $C^{2,α}$ Regularity for Fully Nonlinear Elliptic Equations
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