# Shape Optimization Problems with Internal Constraint

Bucur, Dorin and Buttazzo, Giuseppe and Velichkov, Bozhidar (2011) Shape Optimization Problems with Internal Constraint. arXiv .

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## Abstract

We consider shape optimization problems with internal inclusion constraints, of the form $$\min\big\{J(\Omega)\ :\ \Dr\subset\Omega\subset\R^d,\ |\Omega|=m\big\},$$ where the set $\Dr$ 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.

Item Type: Article Imported from arXiv Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica Dipartimenti (from 2013) > DIPARTIMENTO DI MATEMATICA dott.ssa Sandra Faita 05 Aug 2013 12:46 05 Aug 2013 12:46 http://eprints.adm.unipi.it/id/eprint/1337

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