ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2006 - Volume , Issue 04  

Research Article

Asymptotics of an optimal compliance-location problem

Buttazzo, Giuseppea1, Santambrogio, Filippoa2 and Varchon, Nicolasa3

a1  Università di Pisa, Dip. di Matematica, Largo B. Pontecorvo, 5, 56127 Pisa, Italy; buttazzo@dm.unipi.it

a2  Scuola Normale Superiore, Classe di Scienze, Piazza dei Cavalieri, 7, 56126 Pisa, Italy; santambrogio@sns.it

a3  Collège Condorcet de Bresles, 60510 Bresles, France; nicolasvarchon@netscape.net

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 Γ-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.

(Received July 23 2005)

(Online publication October 11 2006)

Key Words:

  • Compliance;
  • optimal location;
  • shape optimization;
  • Γ-convergence.

Mathematics Subject Classification:

  • 49J45;
  • 49Q10;
  • 74P05