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The Dirichlet problem for a thin rectangle

Published online by Cambridge University Press:  20 January 2009

J. K. Knowles
J. K. Knowles
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California
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We consider the Dirichlet problem for Laplace's equation in a rectangle with a view toward determining the asymptotic behaviour of the solution for the case in which the width of the rectangle is small in comparison with its length. Although the construction of an explicit representation of the solution is an elementary matter, the resulting formula is inconvenient for present purposes, and we accordingly proceed along different lines.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 4 , December 1967 , pp. 315 - 320
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

REFERENCES

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