International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 581-586

Eigenvalues of the negative Laplacian for arbitrary multiply connected domains

E. M. E. Zayed

Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

Received 6 October 1994; Revised 17 January 1995

Copyright © 1996 E. M. E. Zayed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.