Calculus of Variations and Geometric Measure Theory

L. Sigalotti

Asymptotic analysis of periodically perforated nonlinear media at the critical exponent

created by sigalotti on 04 Feb 2008
modified on 08 May 2010


Published Paper

Inserted: 4 feb 2008
Last Updated: 8 may 2010

Journal: Comm. Cont. Math.
Volume: 11
Number: 6
Pages: 1009-1033
Year: 2009


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