# Asymptotic analysis of periodically perforated nonlinear media at the critical exponent

created by sigalotti on 04 Feb 2008
modified on 08 May 2010

[BibTeX]

Published Paper

Inserted: 4 feb 2008
Last Updated: 8 may 2010

Journal: Comm. Cont. Math.
Volume: 11
Number: 6
Pages: 1009-1033
Year: 2009

Abstract:

We give a $\Gamma$-convergence result for vector-valued nonlinear energies defined on periodically perforated domains. We consider integrands with $n$-growth where $n$ is the space dimension, showing that there exists a critical scale for the perforations such that the $\Gamma$-limit is non-trivial. We prove that the limit extra-term is given by a formula of homogenization type, which simplifies in the case of $n$-homogeneous energy densities.