Calculus of Variations and Geometric Measure Theory
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M. Barchiesi

Multiscale homogenization of convex functionals with discontinuous integrand

created by barchiesi on 06 Jul 2005
modified on 12 Jan 2012


Published Paper

Inserted: 6 jul 2005
Last Updated: 12 jan 2012

Journal: J. Convex Anal.
Volume: 14
Number: 1
Pages: 205-226
Year: 2007


This article is devoted to obtain the $\Gamma$-limit, as $\epsilon$ tends to zero, of the family of functionals $$F{\epsilon}(u)=\int{\Omega}f\Bigl(x,\frac{x}{\epsilon},..., \frac{x}{\epsilonn},\nabla u(x)\Bigr)dx\,,$$ 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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