International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 591-598
Hearing the shape of membranes: further results
Department of Mathematics, Zagazig University, Faculty of Science, Zagazig, Egypt
Received 18 January 1989; Revised 5 May 1989
Copyright © 1990 E. M. E. Zayed. 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 Laplacian in , or , is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions on (or ), where and , are parts of the boundaries of these domains respectively, while , are positive constants.