Journal of Convex Analysis 15 (2008), No. 4, 655--676
Copyright Heldermann Verlag 2008
Asymptotic Analysis of Periodically Perforated Nonlinear Media Close to the Critical Exponent
Dip. di Matematica, UniversitÓ di Roma "La Sapienza", Piazzale A. Moro 2, 00185 Roma, Italy
We give a Γ-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 Γ-limit is always trivial.
Keywords: Gamma-convergence, perforated domains, critical exponent.
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