
Journal of Convex Analysis 14 (2007), No. 1, 205226 Copyright Heldermann Verlag 2007 Multiscale Homogenization of Convex Functionals with Discontinuous Integrand Marco Barchiesi S.I.S.S.A., Via Beirut 24, 34014 Trieste, Italy barchies@sissa.it [Abstractpdf] \newcommand{\e}{\varepsilon} This article is devoted to obtain the $\Gamma$limit, as $\e$ tends to zero, of the family of functionals \begin{equation*} u\mapsto\int_{\Omega}f\Bigl(x,\frac{x}{\e}, \ldots, \frac{x}{\e^n}, \nabla u(x)\Bigr)dx , \end{equation*} where $f=f(x, y^1, \ldots, y^n, z)$ is periodic in $y^1, \ldots, y^n$, convex in $z$ and satisfies a very weak regularity assumption with respect to $x, y^1, \ldots, y^n$. We approach the problem using the multiscale Young measures. Keywords: convexity, discontinuous integrands, iterated homogenization, periodicity, multiscale convergence, Young measures, Gammaconvergence MSC: 28A20, 35B27, 35B40, 74Q05 [ Fulltextpdf (261 KB)] for subscribers only. 