Time-interior gradient estimates for quasilinear parabolic equations

TL;DR

This paper establishes gradient bounds for smooth solutions of various quasilinear parabolic equations, including anisotropic mean curvature flows, based on oscillation and elapsed time, enhancing understanding of their regularity properties.

Contribution

It provides new gradient estimates for a broad class of quasilinear parabolic equations, including geometric flows, in terms of oscillation and time.

Findings

Gradient bounds depend on oscillation and elapsed time.

Applicable to Dirichlet and Neumann boundary conditions.

Includes anisotropic mean curvature flow cases.

Abstract

Bounded smooth solutions of the Dirichlet and Neumann problems for a wide variety of quasilinear parabolic equations, including graphical anisotropic mean curvature flows, have gradient bounded in terms of oscillation and elapsed time.