Nonlinear stochastic homogenization in Orlicz spaces and applications

TL;DR

This paper explores the use of ergodic theory in nonlinear stochastic homogenization within Orlicz spaces, applying continuum percolation models and Khruslov's homogenization method to analyze inhomogeneous random media.

Contribution

It extends stochastic homogenization techniques to Orlicz spaces and demonstrates their application to complex random media modeled by continuum percolation.

Findings

Examples of inhomogeneous, random media based on continuum percolation models.

Application of ergodic theory to integral functionals in Orlicz spaces.

Homogenization results using Khruslov's method for complex media.

Abstract

In this paper we are interested in the application of ergodic theory in integral functionals defined in generalizes Sobolev-Orlicz spaces. We provide examples of inhomogeneous, random media based on continuum percolation models that have been introduced in a previous paper. Finally we apply the limit theorem to the homogenization method introduced by E. Khruslov.