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Allowed to fasten, say, one-half of a drum's boundary, which half produces the lowest or highest bass note? The answer is a natural limit of solutions to a family of extremal Robin problems for the least eigenvalue of the Laplacian. We produce explicit extremizers when the drum is a disk, while, for general shapes, we establish existence and necessary(More)
Permitted to fasten an elastic body on but half of its boundary, which portion should be fastened in order to minimize the work done by a specified load? For both plates and planar sheets we establish the existence of a unique solution to a relaxed version of the problem and present the results of a detailed numerical investigation. 1 Introduction We(More)
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