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

2019/01/18 by Lian, Yuanyuan, Zhang, Kai
#35B65 #35D40 #35J25 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.06060

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 ∂ Ω is C^1,α (or C^2,α) at x₀∈ ∂ Ω, the solution is C^1,α (or C^2,α) at x₀. Our results are new even for the Laplace equation. Moreover, our proofs are simple.

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