2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102058This article is devoted to obtain the $Γ$-limit, as $ε$ tends to zero, of the family of functionals $$F_ε(u)=\int_Ωf\Bigl(x,\frac{x}ε,..., \frac{x}{ε^n},\nabla u(x)\Bigr)dx$$, 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.18 pages; a slight change in the title; to be published in J. Convex Anal. 14 (2007), No. 2Analysis of PDEs28A20, 35B27, 35B40, 74Q05text