International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1997 / Article

Open Access

Volume 20 |Article ID 921807 | https://doi.org/10.1155/S0161171297000513

E. M. E. Zayed, "Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions", International Journal of Mathematics and Mathematical Sciences, vol. 20, Article ID 921807, 6 pages, 1997. https://doi.org/10.1155/S0161171297000513

Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

Received08 Jun 1994
Revised21 Mar 1996

Abstract

The spectral function Θ(t)=i=1exp(tλj), where {λj}j=1 are the eigenvalues of the negative Laplace-Beltrami operator Δ, is studied for a compact Riemannian manifold Ω of dimension “k” with a smooth boundary Ω, where a finite number of piecewise impedance boundary conditions (ni+γi)u=0 on the parts Ωi(i=1,,m) of the boundary Ω can be considered, such that Ω=i=1mΩi, and γi(i=1,,m) are assumed to be smooth functions which are not strictly positive.

Copyright © 1997 Hindawi Publishing Corporation. 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.


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