$C^{1,\alpha }$ Regularity for degenerate fully nonlinear elliptic equations with Neumann boundary conditions

Abstract

In this paper, we establish $C^{1,\alpha }$ regularity upto the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. Our main result Theorem 2.1 constitutes the boundary analogue of the interior $C^{1,\alpha }$ regularity result established in [21] for equations with similar structural assumptions. The proof of our main result is achieved via compactness arguments combined with new boundary Hölder estimates for equations which are uniformly elliptic when the gradient is either small or large.

revised version of the file, a few references added