ASYMPTOTIC ANALYSIS OF PERIODICALLY-PERFORATED NONLINEAR MEDIA AT THE CRITICAL EXPONENT

Abstract

We give a Γ-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 Γ-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.