Random homogenization of p-Laplacian with obstacles in perforated domain

TL;DR

This paper investigates the homogenization process of the p-Laplacian operator in perforated domains with randomly sized holes, assuming stationary ergodic p-capacity, to understand effective behavior in complex media.

Contribution

It introduces a novel homogenization framework for p-Laplacian problems with randomly distributed obstacles in perforated domains, considering ergodic properties of hole capacities.

Findings

Derived effective equations for the homogenized p-Laplacian

Established conditions for convergence in random perforated domains

Extended homogenization techniques to stochastic obstacle configurations

Abstract

In this paper,we will study the homogenization of $p$-Laplacian with obstacles in perforated domain, where the holes are periodically distributed and have random size. And we also assume that the $p$-capacity of each hole is stationary ergodic.