Multiscale homogenization of convex functionals with discontinuous integrand

Marco Barchiesi

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Multiscale homogenization of convex functionals with discontinuous integrand

Marco Barchiesi

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Abstract

This 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.

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BibTeX RIS

Marco Barchiesi. 2006-01-12. Multiscale homogenization of convex functionals with discontinuous integrand. https://arxiv.org/abs/math/0506409

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