Asymptotic analysis of periodically-perforated nonlinear media at and close to the critical exponent

We give a general P-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 nontrivial size of the perforation (exponential and mixed polynomialexponential), and one where the Gamma-limit is always trivial.