Geodesic
Multiscale Homogenization of Convex Functionals with Discontinuous Integrand
Journal of convex analysis, Tome 14 (2007) no. 1, pp. 205-226

Voir la notice de l'article provenant de la source Heldermann Verlag

\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.
Classification : 28A20, 35B27, 35B40, 74Q05
Mots-clés : convexity, discontinuous integrands, iterated homogenization, periodicity, multiscale convergence, Young measures, Gamma-convergence 
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     author = {M. Barchiesi},
     title = {Multiscale {Homogenization} of {Convex} {Functionals} with {Discontinuous} {Integrand}},
     journal = {Journal of convex analysis},
     pages = {205--226},
     publisher = {mathdoc},
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     number = {1},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_1_JCA_2007_14_1_a14/}
}
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M. Barchiesi. Multiscale Homogenization of Convex Functionals with Discontinuous Integrand. Journal of convex analysis, Tome 14 (2007) no. 1, pp. 205-226. http://geodesic.mathdoc.fr/item/JCA_2007_14_1_JCA_2007_14_1_a14/