Local estimates for elliptic equations arising in conformal geometry

TL;DR

This paper establishes local gradient and second derivative estimates for solutions to fully nonlinear elliptic equations related to Yamabe type problems involving higher order curvatures on manifolds with geodesic boundaries.

Contribution

It provides new local regularity estimates for solutions to complex elliptic equations in conformal geometry, extending previous results to higher order curvature problems.

Findings

Proved local gradient estimates for solutions.

Established second derivative bounds.

Applied results to Yamabe type problems.

Abstract

In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations associated with the problems.