International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 245-254
doi:10.1155/S0161171295000305
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
Abstract
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.