Regularity for fully nonlinear elliptic equations with oblique boundary conditions

Abstract

In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise $C^{\alpha }$, $C^{1,\alpha }$ and $C^{2,\alpha }$ regularity. As byproducts, we also prove the A-B-P maximum principle, Harnack inequality, uniqueness and solvability of the equations.