C^{1,α} and Glaeser type estimates

Abstract

In this paper we are concerned with gradient estimates for viscosity solutions of fully nonlinear second order elliptic equations of the form F(D^2u) = f with bounded right-hand side. We generalize to a nonlinear setting the results of Yan Yan Li and Louis Nirenberg [12] about the so-called Glaeser estimate. We improve also some qualitative results in this direction contained in [4].

Keywords

• gradient estimates
• elliptic equations
• viscosity solutions