Fully nonlinear, uniformly elliptic equations under natural structure conditions

Abstract

We derive first and second derivative estimates for classical solutions of fully nonlinear, uniformly elliptic equations which are subject to natural structure conditions analogous to those proposed and treated by Ladyzhenskaya and Ural’tseva for quasilinear equations. As an application we extend recent work of Evans and Lions on the Bellman equation for families of linear operators to families of quasilinear operators.