Calculus of Variations and Geometric Measure Theory
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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


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