International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1990 / Article

Open Access

Volume 13 |Article ID 646870 | 8 pages | https://doi.org/10.1155/S0161171290000825

Hearing the shape of membranes: further results

Received18 Jan 1989
Revised05 May 1989

Abstract

The spectral function θ(t)=m=1exp(tλm), t>0 where {λm}m=1 are the eigenvalues of the Laplacian in Rn, n=2 or 3, is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions ur+γju=0 on Γj (or Sj), j=1,,J where Γj and Sj, j=1,,J are parts of the boundaries of these domains respectively, while γj, j=1,,J are positive constants.

Copyright © 1990 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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