International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 245-254

On the spectrum of the negative Laplacian for general doubly-connected bounded domains

E. M. E. Zayed and A. I. Younis

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

Received 17 June 1993; Revised 6 June 1994

Copyright © 1995 E. M. E. Zayed and A. I. Younis. 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.


This paper is devoted to asymptotic formulas for functions related with the spectrum of the standard Laplace operator in two and three dimensional bounded doubly connected domains with impedance boundary conditions, where the impedances are assumed to be positive functions. Moreover, asymptotic expressions for the difference of eigenvalues related to impedance boundary value problems with different impedances are derived. Further results may be obtained.