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Some Aspects of Uniqueness for Solutions to Boundary Problems†

Published online by Cambridge University Press:  20 January 2009

M. H. Martin
M. H. Martin
Affiliation:
Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland, U.S.A.
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The solution to the boundary problem

where r is the distance of point (x, y) from the origin, and h is a given function the arc length s along the unit circle r = 1, is not necessarily unique, Boggio (1), Weinstein (2), Stoker (3), Martin (4). Indeed if h is a positive integer m is known that the only solutions regular analytic for r≦1 are

where r, θ denote polar coordinates and A, B are arbitrary constants.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 25 - 35
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

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