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We deal with the following eigenvalue optimization problem: Given a bounded domain D ⊂ R 2 , how to place an obstacle B of fixed shape within D so as to maximize or minimize the fundamental eigenvalue λ 1 of the Dirich-let Laplacian on D \ B. This means that we want to extremize the function ρ → λ 1 (D \ ρ(B)), where ρ runs over the set of rigid motions… (More)

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