Homogenization and continuum percolation

TL;DR

This paper introduces continuum percolation theory as a new approach to homogenization problems in elliptic equations, aiming to extend results from periodic to ergodic non-periodic domains.

Contribution

It develops a framework for applying continuum percolation to homogenization, broadening the scope beyond periodic settings.

Findings

Extended homogenization results to ergodic non-periodic domains.

Established continuum percolation as a tool for elliptic equations.

Improved understanding of homogenization in complex domains.

Abstract

We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains using modeling for non-periodic domains with certain ergodic properties.