Multiscale homogenization of convex functionals with discontinuous integrand

Details Multiscale homogenization of convex functionals with discontinuous integrand Multiscale homogenization of convex functionals with discontinuous integrand

2005-06-20

arxiv.org/abs/math/0506409v3

Mathematics

Analysis of PDEs

18 pages; a slight change in the title; to be published in J. Convex Anal. 14 (2007), No. 2

Scientific paper

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.

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