Perforated Domains Close to the Critical Exponent

Laura Sigalotti
University of Rome ``La Sapienza''

Abstract: 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.