On a gradient maximum principle for some quasilinear parabolic equations on convex domains

TL;DR

This paper proves a maximum principle for the spatial gradient of solutions to certain quasilinear parabolic equations with Neumann boundary conditions on convex domains, aiding understanding of solution behavior.

Contribution

It introduces a gradient maximum principle for quasilinear parabolic equations on convex domains, extending previous maximum principles to gradient estimates.

Findings

Gradient maximum principle established for solutions.

Applicable to classical solutions with Neumann boundary conditions.

Enhances understanding of solution regularity and bounds.

Abstract

We establish a spatial gradient maximum principle for classical solutions to the initial and Neumann boundary value problem of some quasilinear parabolic equations on smooth convex domains.