Shape Optimization Problems with Internal Constraint

created by buttazzo on 12 Sep 2011
modified by velichkov on 23 Apr 2014

[BibTeX]

Published Paper

Inserted: 12 sep 2011
Last Updated: 23 apr 2014

Journal: Ann. I. H. Poincare' Anal. Non Lineaire
Volume: 30
Number: 3
Pages: 467--495
Year: 2013
Links: The final publication is available at http://www.journals.elsevier.com

Abstract:

We consider shape optimization problems with internal inclusion constraints, of the form

$\min\big\{J(\Omega)\ :\ D\subset\Omega\subset\mathbb{R}^d,\ \Omega =m\big\},$

where the set $D$ is fixed, possibly unbounded, and $J$ depends on $\Omega$ via the spectrum of the Dirichlet Laplacian. We analyze the existence of a solution and its qualitative properties, and rise some open questions.