Statistical and Algebraic Properties for the 4-Laplacian via Averaging

TL;DR

This paper develops discrete analogs of mean value principles for the 4-Laplacian, aiding numerical analysis by bridging continuous and discrete approaches.

Contribution

It introduces novel discrete mean value principles specific to the 4-Laplacian, enhancing understanding and computational methods for this operator.

Findings

Discrete mean value principles established for the 4-Laplacian

Connections between continuous and discrete properties demonstrated

Potential improvements in numerical analysis techniques

Abstract

We find discrete analogs to continuous mean value principles that are used in the numerical analysis of the normalized p-Laplacian for particular values of p, specifically when p is 4.