Boundary pointwise C1,α and C2,α regularity for fully nonlinear elliptic equations

In this paper, we obtain the boundary pointwise C-1,C-alpha and C-2,C-alpha regularity for viscosity solutions of fully nonlinear elliptic equations. That is, if partial derivative Omega is C-1,C-alpha(or C-2,C-alpha) at x(0) is an element of partial derivative Omega, the solution is C-1,C-alpha(or C-2,C-alpha) at x(0). Our results are new even for the Laplace equation. Moreover, our proofs are simple. (C) 2020 Elsevier Inc. All rights reserved.