Small perturbations and the eigenvalues of the Laplacian on large bounded domains
Author: Werner Kirsch
Journal: Proc. Amer. Math. Soc. 101 (1987), 509-512
MSC: Primary 35P20; Secondary 35J25, 47F05
MathSciNet review: 908658
Abstract: Denote by the Laplacian on a hypercube in with side length . Also denote by the number of eigenvalues of the operator below . If is a bounded function of compact support, ( on a set of positive measure) then is not bounded as for dimension .
Keywords: Dirichlet Laplacian, small perturbation, eigenvalue distribution
Article copyright: © Copyright 1987 American Mathematical Society