Improved regularity for the parabolic normalized p-Laplace equation

TL;DR

This paper establishes regularity estimates for viscosity solutions to the parabolic normalized p-Laplace equation, demonstrating local Lipschitz continuity of the gradient near p=2 and providing Sobolev space regularity results.

Contribution

It introduces new regularity estimates for solutions to the normalized p-Laplace equation, especially near p=2, using approximation and scaling techniques.

Findings

Gradient of solutions is locally Lipschitz continuous near p=2

Regularity estimates are established in Sobolev spaces

Approximation methods effectively derive regularity results

Abstract

We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments for the normalized p-parabolic operator, we show that the gradient of bounded viscosity solutions is locally asymptotically Lipschitz continuous when $p$ is sufficiently close to 2. In addition, we establish regularity estimates in Sobolev spaces.