Asymptotic analysis of periodically-perforated nonlinear media

AbstractWe give a direct proof of the nonlinear vector-valued variational version of the Cioranescu Murat result on the asymptotic behaviour of Dirichlet problems in perforated domains giving rise to extra terms. Our method is based on a lemma which allows to modify sequences of functions in the vicinity of the perforation, in the spirit of a method proposed by De Giorgi to match boundary conditions. We describe the extra term by a capacitary formula involving a quasiconvexification process. Nonexistence and nonpositive homogeneity phenomena are discussed