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- Steven J. Cox, Paul X. Uhlig
- SIAM Journal on Optimization
- 1999

Abstract. If we are 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… (More)

- SJ Cox, Paul X. Uhlig
- 2001

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.

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)

- Gopalakrishnan Easwaran, Larry E. Parten, Rafael Moras, Paul X. Uhlig
- Applied Mathematics and Computation
- 2010

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