Inserted: 2 feb 2008
Last Updated: 22 mar 2008
Journal: Comptes Rendus Acad. Sci. Paris
Pages: 363 - 367
We give a general $\Gamma$-convergence result for vector-valued non-linear energies defined on perforated domains for integrands with $p$-growth in the critical case $p=n$. We characterize the limit extra term by a formula of homogenization type. We also prove that for $p$ close to $n$ there are three regimes, two with a non trivial size of the perforation (exponential and mixed polynomial-exponential), and one where the $\Gamma$-limit is always trivial.
Keywords: Gamma-convergence, perforated domains, critical exponent, expansion