*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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