Multiscale homogenization of convex functionals with discontinuous integrand
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2005
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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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Journal of Convex Analysis 14 (2007) 205-226