Showing papers by "Steven J. Cox published in 1990"
TL;DR: In this article, the authors characterized the distribution of the two materials in Ω that extremizes the kth eigenvalue of the resulting clamped membrane and showed that these extremizers vary continuously with the proportion of the components.
Abstract: Given an open bounded connected set Ω ⊂R
N
and a prescribed amount of two homogeneous materials of different density, for smallk we characterize the distribution of the two materials in Ω that extremizes thekth eigenvalue of the resulting clamped membrane. We show that these extremizers vary continuously with the proportion of the two constituents. The characterization of the extremizers in terms of level sets of associated eigenfunctions provides geometric information on their respective interfaces. Each of these results generalizes toN dimensions the now classical one-dimensional work of M. G. Krein.
82 citations