Inserted: 3 feb 2008
Last Updated: 8 may 2010
Journal: J. Convex Anal.
We give a $\Gamma$-convergence result for vector-valued nonlinear energies defined on periodically perforated domains. We consider integrands with $p$-growth for $p$ converging to the space dimension $n$. We prove that for $p$ close to the critical exponent $n$ there are three regimes, two with a non-trivial size of the perforations (exponential and mixed polynomial-exponential) and one where the $\Gamma$-limit is always trivial.
Keywords: Gamma-convergence, perforated domains, critical exponent