Homogenization for the Poisson equation in domains perforated by random closed sets

TL;DR

This paper investigates the homogenization of the Poisson equation in domains with randomly distributed holes, revealing a strange term effect and establishing corrector results under stationarity assumptions.

Contribution

It introduces a novel homogenization framework for perforated domains with germ-grain processes, highlighting the constant potential in the homogenized equation despite nonstationary hole distributions.

Findings

Strange term effect identified in the homogenized Poisson equation.

Homogenization results hold under stationarity of hole capacities.

Corrector results established for the model.

Abstract

We study the homogenization of the Poisson equation in randomly perforated domains and obtain the strange term effect in the homogenized equation. The perforations are modeled by rescaled germ-grain processes, and the main assumption is stationarity of the capacities of the holes. We emphasize that the potential in the homogenized equation is constant, despite the possibly nonstationary spatial distribution of the holes. We also establish corrector results.