Showing papers by "Steven J. Cox published in 2003"
TL;DR: The paper produces explicit extremizers when the drum is a disk, while, for general shapes, existence and necessary conditions are established, and a pair of numerical methods are built and test.
Abstract: 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 conditions, and build and test a pair of numerical methods.
18 citations