Abstract: We give a general -convergence result for
vector-valued non-linear energies defined on perforated domains for integrands
with
-growth in the critical case
. We characterize the limit extra
term by a formula of homogenization type. We also prove that for
close to
there are three regimes, two with a non trivial size of the perforation
(exponential and mixed polynomial-exponential), and one where the
-limit is always trivial.