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Issue ESAIM: COCV
Volume 12, Number 4, October 2006
Page(s) 752 - 769
DOI 10.1051/cocv:2006020
Published online 11 October 2006

ESAIM: COCV, October 2006, Vol. 12, pp. 752-769
DOI: 10.1051/cocv:2006020

Asymptotics of an optimal compliance-location problem

Giuseppe Buttazzo1, Filippo Santambrogio2 and Nicolas Varchon3

1  Università di Pisa, Dip. di Matematica, Largo B. Pontecorvo, 5, 56127 Pisa, Italy; buttazzo@dm.unipi.it
2  Scuola Normale Superiore, Classe di Scienze, Piazza dei Cavalieri, 7, 56126 Pisa, Italy; santambrogio@sns.it
3  Collège Condorcet de Bresles, 60510 Bresles, France; nicolasvarchon@netscape.net


(Received July 23, 2005. Published online 11 October 2006.)

Abstract
We consider the problem of placing a Dirichlet region made by n small balls of given radius in a given domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look for the $\Gamma-$limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.


Mathematics Subject Classification. 49J45, 49Q10, 74P05.

Key words: Compliance, optimal location, shape optimization, $\Gamma-$convergence.


© EDP Sciences, SMAI 2006


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