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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

(1) Boggio, T., Suite funzioni di variable complessa ui un'area circolari, Rendiconti della R. Accademia de Torino, 47 (1912), 22–37.Google Scholar
(2) Weinstein, A., Fluid motion with free boundaries, Proceedings of the First Symposium in Applied Mathematics, American Mathematical Society (1949), 1–18.CrossRefGoogle Scholar
(3) Stoker, J. J., Water waves, Interscience (1957), 38–41.Google Scholar
(4) Martin, M. H., Linear and nonlinear boundary problems for harmonic functions, Proceedings American Mathematical Society, 10 (1959), 258–266.CrossRefGoogle Scholar
(5) Goursat, E., Lecons sur l'intégration des équations aux dérivées partielles du premier ordre, Paris (1921), 134–153.Google Scholar
(6) Whittaker, E. T., A Course of Modern Analysis (Cambridge, 4th Edition, 1927), 302–319.Google Scholar