Second order estimates for Hessian equations of parabolic type on Riemannian manifolds

TL;DR

This paper develops second order estimates for solutions to fully nonlinear Hessian parabolic equations on Riemannian manifolds, providing a broad framework applicable to various PDEs under general conditions.

Contribution

It introduces a new method for obtaining second order estimates for Hessian type fully nonlinear parabolic equations on Riemannian manifolds, applicable to a wide class of PDEs.

Findings

Established second order estimates for solutions to Hessian parabolic equations.

Techniques applicable to a broad range of nonlinear PDEs.

Results hold under very general conditions.

Abstract

In this paper, we establish the second order estimates of solutions to the first initial-boundary value problem for general Hessian type fully nonlinear parabolic equations on Riemannian manifolds. The techniques used in this article can work for a wide range of fully nonlinear PDEs under very general conditions.