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arXiv · 1109.2413

Shape Optimization Problems with Internal Constraint

Dorin Bucur·Giuseppe Buttazzo·Bozhidar Velichkov
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Abstract

We consider shape optimization problems with internal inclusion constraints, of the form $$\min\big\{J(Ω)\ :\ \Dr\subsetΩ\subset\R^d,\ |Ω|=m\big\},$$ where the set $\Dr$ is fixed, possibly unbounded, and $J$ depends on $Ω$ via the spectrum of the Dirichlet Laplacian. We analyze the existence of a solution and its qualitative properties, and rise some open questions.

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Dorin Bucur, Giuseppe Buttazzo, Bozhidar Velichkov. 2011-09-12. Shape Optimization Problems with Internal Constraint. https://arxiv.org/abs/1109.2413

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