Abstract

This article is devoted to obtain the Γ\Gamma-limit, as ε\e tends to zero, of the family of functionals u↦∫Ωf(x,xε,…,xεn,∇u(x))dx,u\mapsto\int_{\Omega}f\Bigl(x,\frac{x}{\e}, \ldots, \frac{x}{\e^n}, \nabla u(x)\Bigr)dx, where f=f(x,y1,…,yn,z)f=f(x, y^1, \ldots, y^n, z) is periodic in y1,…,yny^1, \ldots, y^n, convex in zz and satisfies a very weak regularity assumption with respect to x,y1,…,ynx, y^1, \ldots, y^n. We approach the problem using the multiscale Young measures.

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Keywords

  • convexity
  • discontinuous integrands
  • iterated homogenization
  • periodicity
  • multiscale convergence
  • Young measures
  • Gamma-convergence

Mathematics Subject Classification

28A20, 35B27, 35B40, 74Q05

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Suggested citation

M. Barchiesi. “Multiscale Homogenization of Convex Functionals with Discontinuous Integrand.” Journal of Convex Analysis 14 (2007), No. 1, 205–226. https://doi.org/10.68381/jca14015

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.