Interior and boundary gradient estimates for Neumann problem of fully nonlinear Hessian equations

TL;DR

This paper establishes interior and boundary gradient estimates for solutions to the Neumann problem of fully nonlinear Hessian equations on Riemannian manifolds, advancing understanding of boundary behavior in nonlinear PDEs.

Contribution

It provides new a priori gradient estimates for admissible solutions, combining interior and boundary analysis on Riemannian manifolds.

Findings

Interior gradient estimates derived for admissible solutions.

Boundary gradient estimates obtained from interior estimates.

Results applicable to fully nonlinear Hessian equations on Riemannian manifolds.

Abstract

In this paper we study the {\it a priori} gradient estimates for admissible solutions to Neumann boundary value problem of fully nonlinear Hessian equations on Riemannian manifolds. We firstly derive an interior gradient estimates for admissible solutions, then we obtain boundary gradient estimates based on the interior gradient estimates we have got.