Perforated Domains Close to the Critical Exponent Laura Sigalotti University of Rome “La Sapienza”

                   sigalott@mat.uniroma1.it

Abstract: We give a general Γ-convergence result for vector-valued nonlinear 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 Γ-limit is always trivial.