Eigenvalues of the Laplacian for rectilinear regions
Hans P. W. Gottlieb · ANZIAM Journal · 1988
Abstract From a knowledge of the eigenvalue spectrum of the Laplacian on a domain, one may extract information on the geometry and boundary conditions by analysing the asymptotic expansion of a spectral function. Explicit calculations are performed for isosceles right-angle triangles with Dirichlet or Neumann boundary conditions, yielding in particular the corner angle terms. In three dimensions, right prisms are dealt with, including the solid vertex terms.