Published Paper

Inserted: 6 jul 2005
Last Updated: 12 jan 2012

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

Abstract:

This article is devoted to obtain the $\Gamma$-limit, as $\epsilon$ tends to zero, of the family of functionals $$F_{\epsilon}(u)=\int_{{\Omega}f\Bigl}(x,\frac{x}{\epsilon},..., \frac{x}{\epsilon^n},\nabla u(x)\Bigr)dx\,,$$ 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

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