The Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds

TL;DR

This paper establishes the existence of $C^{1,1}$ solutions for the Dirichlet problem involving degenerate fully nonlinear elliptic equations on Riemannian manifolds, expanding the understanding of such equations in geometric contexts.

Contribution

It provides new existence results for degenerate fully nonlinear elliptic equations on Riemannian manifolds, a setting less explored in previous literature.

Findings

Existence of $C^{1,1}$ solutions under certain conditions

Extension of elliptic PDE theory to Riemannian manifolds

Framework for handling degeneracy in nonlinear elliptic equations

Abstract

We derive the existence of $C^{1,1}$-solutions to the Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds under appropriate assumptions.