Homogenization for the Poisson equation in domains perforated by random closed sets
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 23 February 2026
- Language
- EN
- Document type
- Preprint