# On some rescaled shape optimization problems

Buttazzo, Giuseppe and Wagner, Alfred (2009) On some rescaled shape optimization problems. arXiv .

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## Abstract

SUMMARY We consider Cheeger-like shape optimization problems of the form $$\min\big\{|\Omega|^\alpha J(\Omega) : \Omega\subset D\big\}$$ where $D$ is a given bounded domain and $\alpha$ is above the natural scaling. We show the existence of a solution and analyze as $J(\Omega)$ the particular cases of the compliance functional $C(\Omega)$ and of the first eigenvalue $\lambda_1(\Omega)$ of the Dirichlet Laplacian. We prove that optimal sets are open and we obtain some necessary conditions of optimality.

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 12:48 05 Aug 2013 12:48 http://eprints.adm.unipi.it/id/eprint/1330

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