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Mixed Boundary-Value Problems in Potential Theory

Published online by Cambridge University Press:  20 January 2009

A. H. England
A. H. England
Affiliation:
Department of Theoretical Mechanics, University of Nottingham
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The problems associated with finding solutions of Laplace's equation subject to mixed boundary conditions have attracted much attention and, as a consequence, a variety of analytical techniques have been developed for the solution of such problems. Sneddon (1) has given a comprehensive account of these techniques. The object of this note is to draw attention to some simple orthogonal polynomial solutions to the most basic mixed boundary-value problems in two and threedimensional potential theory. These solutions have the advantage that most quantities of physical interest are easily evaluated in terms of known functions. Two-dimensional problems are considered in §2 and axially-symmetric three-dimensional problems in §3.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 91 - 98
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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