On Some Rescaled Shape Optimization Problems
نویسنده
چکیده
We consider Cheeger-like shape optimization problems of the form min { |Ω|J(Ω) : Ω ⊂ D } 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 λ1(Ω) of the Dirichlet Laplacian. We prove that optimal sets are open and we obtain some necessary conditions of optimality.
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