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
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.