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{\it Perforated Domains Close to the Critical Exponent}

{\bf Laura Sigalotti}\\ 
University of Rome ``La Sapienza''\\
{\tt sigalott@mat.uniroma1.it}
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\noindent {\bf Abstract}:  We give a general $\Gamma$-convergence result for
vector-valued non-linear energies defined on perforated domains for integrands
with $p$-growth in the critical case $p=n$.  We characterize the limit extra
term by a formula of homogenization type. We also prove that for $p$ close to
$n$ there are three regimes, two with a non trivial size of the perforation
(exponential and mixed polynomial-exponential), and one where the
$\Gamma$-limit is always trivial.

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