Calculus of Variations and Geometric Measure Theory

J. Matias - M. Morandotti

Homogenization problems in the Calculus of Variations: an overview

created by morandott on 18 Mar 2015
modified on 07 Feb 2017


Published Paper

Inserted: 18 mar 2015
Last Updated: 7 feb 2017

Journal: São Paulo Journal of Mathematical Sciences
Volume: 9
Number: 2
Pages: 162-180
Year: 2015
Doi: 10.1007/s40863-015-0016-2

Preprint SISSA 13/2015/MATE


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.

Keywords: Homogenization, calculus of variations, $\mathcal{A}$-quasiconvexity, representation of integral functionals