Gradient estimates for an orthotropic nonlinear diffusion equation in the Heisenberg group

TL;DR

This paper establishes local Lipschitz regularity for solutions to a specific class of nonlinear diffusion equations in the Heisenberg group, expanding understanding of their regularity properties in sub-Riemannian geometry.

Contribution

It provides the first regularity results for orthotropic p-Laplacian equations in the Heisenberg group for 2 ≤ p ≤ 4.

Findings

Proves local Lipschitz regularity for weak solutions

Extends regularity theory to orthotropic nonlinear equations in sub-Riemannian settings

Addresses a range of p-values from 2 to 4

Abstract

We prove local Lipschitz regularity for weak solutions to a parabolic orthotropic $p$-Laplacian-type equation in the Heisenberg group $\Hn$, for the range $2\leq p\leq4$.