Reiterated $\Sigma$-Convergence In Orlicz Setting and Applications

TL;DR

This paper extends the concept of reiterated $\\Sigma$-convergence to Orlicz-Sobolev spaces, enabling homogenization analysis of multiscale problems with nonlinear degenerate elliptic operators and nonstandard growth in a deterministic setting.

Contribution

It introduces a new framework for reiterated $\Sigma$-convergence in Orlicz spaces and applies it to homogenize complex nonlinear operators with nonstandard growth.

Findings

Extended reiterated $\Sigma$-convergence to Orlicz-Sobolev spaces.

Applied the framework to homogenize nonlinear degenerate elliptic operators.

Derived concrete homogenization results for various structured problems.

Abstract

The concept of reiterated $\Sigma$-convergence (and more generally of multiscale $\Sigma$-convergence) is extended to framework of Orlicz-Sobolev spaces, in order to deals with homogenization of multiscales problems in general deterministic setting and whose solutions leads in this type of spaces. This concept relies on the notion of reiterated homogenization supralgebra that we will assumed being ergodic. An application to the deterministic reiterated homogenization of nonlinear degenerate elliptic operators with nonstandard growth is given and some concrete homogenization problems following varied structure hypothesis are deduce from this latter.