Boundary Pointwise $C^{1,α}$ and $C^{2,α}$ Regularity for Fully Nonlinear Elliptic Equations

Yuanyuan Lian; Kai Zhang

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arXiv · 1901.06060

Boundary Pointwise $C^{1,α}$ and $C^{2,α}$ Regularity for Fully Nonlinear Elliptic Equations

Yuanyuan Lian·Kai Zhang

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Abstract

In this paper, we obtain the boundary pointwise $C^{1,α}$ and $C^{2,α}$ regularity for viscosity solutions of fully nonlinear elliptic equations. I.e., If $\partial Ω$ is $C^{1,α}$ (or $C^{2,α}$) at $x_0\in \partial Ω$, the solution is $C^{1,α}$ (or $C^{2,α}$) at $x_0$. Our results are new even for the Laplace equation. Moreover, our proofs are simple.

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BibTeX RIS

Yuanyuan Lian, Kai Zhang. 2019-01-18. Boundary Pointwise $C^{1,α}$ and $C^{2,α}$ Regularity for Fully Nonlinear Elliptic Equations. https://arxiv.org/abs/1901.06060

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