Homogenization problems in the Calculus of Variations: an overview

TL;DR

This paper provides an overview of variational methods used in homogenization problems within the Calculus of Variations, highlighting key theoretical tools and open challenges in the field.

Contribution

It offers a concise summary of classical and modern variational techniques for homogenization, serving as an introductory guide.

Findings

Summarizes fundamental theoretical tools for homogenization

Highlights classical and modern variational methods

Mentions open problems in the field

Abstract

In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.