Calculus of Variations
Asymptotic analysis of periodically-perforated nonlinear media at and close to the critical exponent
[Analyse asymptotique dans l'étude de milieux perforés au voisinage d'un exposant critique]
Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 363-367.

On établit un résultat général de Γ-convergence d'énergies vectorielles nonlinéares définies sur des domaines perforés, dans le cas où l'intégrande est de croissance p, dans le cas critique p=n ; la limite est caractérisée par une formule de type homogénéisation. On démontre également que pour p voisin de n trois régimes sont possibles, deux avec une taille du perforation non triviale (exponentielle et polynomiale-exponentielle), et une taille pour laquelle la Γ-limite est toujours triviale.

We give a general Γ-convergence result for vector-valued nonlinear 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 nontrivial size of the perforation (exponential and mixed polynomial-exponential), and one where the Γ-limit is always trivial.

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Accepté le :
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DOI : 10.1016/j.crma.2008.01.010
Braides, Andrea 1 ; Sigalotti, Laura 2

1 Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, via della ricerca scientifica, 00133 Roma, Italy
2 Dipartimento di Matematica, Università di Roma ‘La Sapienza’, piazzale A.Moro, 00185 Roma, Italy
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Braides, Andrea; Sigalotti, Laura. Asymptotic analysis of periodically-perforated nonlinear media at and close to the critical exponent. Comptes Rendus. Mathématique, Tome 346 (2008) no. 5-6, pp. 363-367. doi : 10.1016/j.crma.2008.01.010. http://www.numdam.org/articles/10.1016/j.crma.2008.01.010/

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