Second order estimates for fully nonlinear elliptic equations with gradient terms on closed Riemannian manifolds

Abstract

Establishing a priori estimates for second derivatives is a key ingredient in the study of fully nonlinear elliptic equations,which is the focus of this paper. We consider a class of second order fully nonlinear equations on closed Riemannian manifolds. In terms of the tangent cone at infinity to the level sets of an associated function which may depend on the solution and its gradient, we introduce a condition to derive second order estimates for solutions of the equation.