Eigenvalues of the Laplacian: an Extension to Higher Dimensions
Elsayed M. E. Zayed · IMA Journal of Applied Mathematics · 1984
The trace function where {λn}n=1∞ are the eigenvalues of the three-dimensional Laplacian, is studied for a variety of domains. The dependence of Θ(t) on the connectivity of domains and the boundary conditions is analysed. Particular attention is given for a spherical shell.