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The Quarterly Journal of Mechanics and Applied Mathematics 1997 50(3):457-466; doi:10.1093/qjmam/50.3.457
© 1997 by Oxford University Press
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A CLASS OF DIRICHLET PROBLEMS FOR THE HELMHOLTZ EQUATION

W. E. WILLIAMS

( Department of Mathematical and Computing Sciences, University of Surrey Guildford, Surrey GU2 5XH )

A formal solution is obtained to a class of Dirichlet problems for Helmholtz's equation within a corner. It is shown that, for corner angles p{pi}/q, where p and q are relatively prime integers, the expansions of the solutions in the neighbourhood of the corner include a term proportional to rq In (r), where r is the distance from the corner. A sufficient condition to ensure the absence of such terms is given.


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