Shape Optimization Problems with Internal Constraint

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

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.

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