Inserted: 4 feb 2008
Last Updated: 8 may 2010
Journal: Comm. Cont. Math.
We give a $\Gamma$-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 $\Gamma$-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.
Keywords: Gamma-convergence, perforated domains, critical exponent