pointwise boundary ${\mathbf{C}}^{1,\mathbf{\alpha }}$ Estimates for some degenerate fully nonlinear elliptic equations on ${\mathbf{C}}^{1,\mathbf{\alpha }}$ Domains

Abstract

In this paper, we establish pointwise boundary $C^{1,\alpha }$ estimates for viscosity solutions of some degenerate fully nonlinear elliptic equations on $C^{1,\alpha }$ domains. Instead of straightening out the boundary, we utilize the perturbation and compactness techniques.

10 pages