(Two-scale) $W^{1}L^{\Phi}$-gradient Young measures and homogenization of integral functionals in Orlicz-Sobolev spaces

TL;DR

This paper introduces and characterizes two-scale gradient Young measures in Orlicz-Sobolev spaces, providing an integral representation for non-convex energies in homogenization problems with nonstandard growth.

Contribution

It develops a new framework for two-scale gradient Young measures in Orlicz-Sobolev spaces, extending homogenization theory to nonstandard growth conditions.

Findings

Provides a characterization of two-scale gradient Young measures in Orlicz-Sobolev spaces.

Derives an integral representation formula for non-convex energies.

Applies to homogenization problems with nonstandard growth conditions.

Abstract

(Two-scale) gradient Young measures in Orlicz-Sobolev setting are introduced and characterized providing also an integral representation formula for non convex energies arising in homogenization problems with nonstandard growth.