# Reiterated periodic homogenization of integral functionals with convex and nonstandard growth integrands

## TL;DR

This paper extends multiscale periodic homogenization to Orlicz-Sobolev spaces, demonstrating convergence of minimizers of oscillatory problems to those of a homogenized convex functional using reiterated two-scale convergence.

## Contribution

It introduces a novel homogenization framework for convex functionals with nonstandard growth in Orlicz-Sobolev spaces using reiterated two-scale convergence.

## Key findings

- Convergence of minimizers to homogenized problem
- Extension of homogenization to Orlicz-Sobolev setting
- Use of reiterated two-scale convergence method

## Abstract

Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems involving convex functionals, converges to the minimizers of a homogenized problem with a suitable convex function.