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Eigenvalues of the Laplacian for rectilinear regions

Published online by Cambridge University Press:  17 February 2009

H. P. W. Gottlieb
H. P. W. Gottlieb
Affiliation:
School of Science, Griffith University, Nathan, Queensland 4111, Australia.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 3 , January 1988 , pp. 270 - 281
Copyright
Copyright © Australian Mathematical Society 1988

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