Global gradient estimates for a general type of nonlinear parabolic equations

TL;DR

This paper establishes new global gradient estimates for solutions to a broad class of nonlinear parabolic equations, including those in Riemannian geometry, revealing enhanced regularity effects and unifying many classical results.

Contribution

It introduces a unified approach to derive global gradient estimates for diverse nonlinear parabolic equations, extending existing results and capturing additional regularity effects.

Findings

Global gradient estimates valid in the entire domain

Enhanced regularity effects due to specific parabolic data

Unification of many classical results as special cases

Abstract

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the validity of the estimates in the global domain, and it detects several additional regularity effects due to special parabolic data. Moreover, our result comprises a large number of nonlinear sources treated by a unified approach, and it recovers many classical results as special cases.