Calculus of Variations and Geometric Measure Theory

L. Sigalotti

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

created by sigalotti on 03 Feb 2008
modified on 08 May 2010


Published Paper

Inserted: 3 feb 2008
Last Updated: 8 may 2010

Journal: J. Convex Anal.
Volume: 15
Number: 4
Pages: 655-676
Year: 2008


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