Second Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian Manifolds

Abstract

We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet problem on manifolds with boundary without any geometric restrictions to the boundary except being smooth and compact. As applications of these estimates we obtain results on regularity and existence.

Cited by in corpus (7)

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• Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications
• The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation
• Remarks on Hessian quotient equations on Riemannian manifolds
• On the exterior Dirichlet problem for Hessian type fully nonlinear elliptic equations
• Monge-Ampère type equations on almost Hermitian manifolds
• The parabolic split-type Monge-Ampere on split tangent bundle surfaces