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

TL;DR

This paper extends regularity results for parabolic Hessian equations on Riemannian manifolds, broadening the classes of equations under weaker assumptions, advancing the understanding of second order estimates in this context.

Contribution

It generalizes previous regularity results for parabolic Hessian equations on Riemannian manifolds under weaker conditions.

Findings

Established second order estimates for a broader class of parabolic Hessian equations.

Extended regularity results to more general equations on Riemannian manifolds.

Improved understanding of solution behavior under weaker assumptions.

Abstract

The author extends previous results to general classes of equations under weaker assumptions obtained in 2016 by Bao, Dong and Jiao concerning the study of the regularity of solutions for the first initial-boundary value problem for parabolic Hessian equations on Riemannian manifolds.