International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 11, Pages 717-726
The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum in with Robin boundary conditions
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
Received 25 June 1999
Copyright © 2001 E. M. E. Zayed and I. H. Abdel-Halim. 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.
The spectral function , where are the eigenvalues of the two-dimensional negative Laplacian, is studied
for small for a variety of domains, where and . The dependencies of on the connectivity of a domain and the Robin boundary
conditions are analyzed. Particular attention is given to an
arbitrary multiply-connected drum in together with
Robin boundary conditions on its boundaries.