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arXiv · 2602.19579

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

Naoto Sato
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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.

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Naoto Sato. 2026-02-23. Homogenization for the Poisson equation in domains perforated by random closed sets. https://arxiv.org/abs/2602.19579

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