Calculus of Variations and Geometric Measure Theory

A. Braides - L. Sigalotti

Asymptotic analysis of periodically-perforated nonlinear media at and close to the critical exponent

created by braidesa on 02 Feb 2008
modified on 22 Mar 2008


Published Paper

Inserted: 2 feb 2008
Last Updated: 22 mar 2008

Journal: Comptes Rendus Acad. Sci. Paris
Volume: 346
Pages: 363 - 367
Year: 2008


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.

Keywords: Gamma-convergence, perforated domains, critical exponent, expansion