Asymptotics of an optimal compliance-location problem

Abstract

We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the minimization problem, after properly scaling the functionals involved, and to the limit distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.

20 pages with 2 figures; final accepted version (minor changes, some extra details on the positivity assumption on $f$)