*Published Paper*

**Inserted:** 4 feb 2008

**Last Updated:** 8 may 2010

**Journal:** Comm. Cont. Math.

**Volume:** 11

**Number:** 6

**Pages:** 1009-1033

**Year:** 2009

**Abstract:**

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

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