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arXiv · 0911.4561

On some rescaled shape optimization problems

Giuseppe Buttazzo·Alfred Wagner
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Abstract

We consider Cheeger-like shape optimization problems of the form $$\min\big\{|Ω|^αJ(Ω) : Ω\subset D\big\}$$ where $D$ is a given bounded domain and $α$ is above the natural scaling. We show the existence of a solution and analyze as $J(Ω)$ the particular cases of the compliance functional $C(Ω)$ and of the first eigenvalue $λ_1(Ω)$ of the Dirichlet Laplacian. We prove that optimal sets are open and we obtain some necessary conditions of optimality.

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Giuseppe Buttazzo, Alfred Wagner. 2009-11-24. On some rescaled shape optimization problems. https://arxiv.org/abs/0911.4561

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