Convergence of Natural $p$-Means for the $p$-Laplacian in the Heisenberg Group

TL;DR

This paper proves that natural $p$-mean operators uniformly converge to $p$-harmonic functions in bounded domains of the Heisenberg group, including Euclidean $C^{1,1}$ domains, under certain geometric conditions.

Contribution

It establishes the uniform convergence of $p$-mean approximations to $p$-harmonic functions in the Heisenberg group, extending previous results to more general domains.

Findings

Uniform convergence of $p$-mean approximations in the Heisenberg group

Includes Euclidean $C^{1,1}$ domains as special cases

Applicable under intrinsic exterior corkscrew condition

Abstract

In this paper we prove uniform convergence of approximations to $p$-harmonic functions by using natural $p$-mean operators on bounded domains of the Heisenberg group $\mathbb{H}$ which satisfy an intrinsic exterior corkscrew condition. These domains include Euclidean $C^{1,1}$ domains.