Calculus of Variations and Geometric Measure Theory

G. Buttazzo - F. Santambrogio - N. Varchon

Asymptotics of an optimal compliance-location problem

created by santambro on 31 May 2005
modified on 19 Oct 2006


Published Paper

Inserted: 31 may 2005
Last Updated: 19 oct 2006

Journal: ESAIM: COCV
Volume: 12
Number: 4
Pages: 752-769
Year: 2006


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.

Keywords: shape optimization, compliance, optimal location, $\Gamma-$convergence