International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 581-586
doi:10.1155/S0161171296000804
Eigenvalues of the negative Laplacian for arbitrary multiply connected domains
E.M.E. Zayed
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract
The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function ∑k=1∞{μk(σ1,…,σn)+P}−2 as P→∞. Further results may be obtained.