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Singularities of two-dimensional exterior solutions of the Helmholtz equation

Published online by Cambridge University Press:  24 October 2008

R. F. Millar
R. F. Millar
Affiliation:
Radio and Electrical Engineering Division, National Research Council, Ottawa, Canada
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Abstract

A technique for locating possible singularities of two-dimensional ex-terior harmonic functions was discussed in a previous paper. In the present work, the method is generalized to exterior solutions of the Helmholtz equation. Although the procedure deviates in some of its details from the earlier exposition, the conclusions are similar. In particular, it is verified that solutions of the Laplace and Helmholtz equations that satisfy the same Dirichlet boundary condition on the same boundary, possess the same convex hull of singularities. The possibility of extending the method to more general equations is raised.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 175 - 188
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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