Calculus of Variations and Geometric Measure Theory

M. Barchiesi

Multiscale homogenization of convex functionals with discontinuous integrand

created by barchiesi on 06 Jul 2005
modified on 12 Jan 2012


Published Paper

Inserted: 6 jul 2005
Last Updated: 12 jan 2012

Journal: J. Convex Anal.
Volume: 14
Number: 1
Pages: 205-226
Year: 2007


This article is devoted to obtain the $\Gamma$-limit, as $\epsilon$ tends to zero, of the family of functionals $$F{\epsilon}(u)=\int{\Omega}f\Bigl(x,\frac{x}{\epsilon},..., \frac{x}{\epsilonn},\nabla u(x)\Bigr)dx\,,$$ where $f=f(x,y^1,...,y^n,z)$ is periodic in $y^1,...,y^n$, convex in $z$ and satisfies a very weak regularity assumption with respect to $x,y^1,...,y^n$. We approach the problem using the multiscale Young measures.

Keywords: Young Measures, Gamma-convergence, discontinuous integrands, iterated homogenization, multiscale convergence