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Local uniqueness in boundary problems†

Published online by Cambridge University Press:  20 January 2009

M. H. Martin
M. H. Martin
Affiliation:
University of Maryland, College Park, Maryland
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The study of periodic, irrotational waves of finite amplitude in an incompressible fluid of infinite depth was reduced by Levi-Civita (1) to the determination of a function

regular analytic in the interior of the unit circle ρ = 1 and which satisfies the condition

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 23 - 36
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Levi-Civita, T., Détermination rigoureuse des ondes permanentes d’ampleur finie, Math. Ann. 93 (1925), 264–314.CrossRefGoogle Scholar
(2) Lichtenstein, L., Nichtlineare Integralgleichungen (Leipzig, 1931), 47–54.Google Scholar
(3) Stoker, J. J., Water Waves (New York, 1957), 513–543.Google Scholar
(4) Dunninger, D. and Martin, M. H., On a uniqueness question of Levi-Civita, Atti Accad. Naz. Lincei Rend. CI. Sci. Fis. Mat. Natur. (8) 41 (1966), 452–459.Google Scholar
(5) Cushing, J., Local uniqueness for harmonic functions under nonlinear boundary conditions, University of Maryland doctoral thesis (1968).Google Scholar
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(7) Dunninger, D., Uniqueness and comparison theorems for harmonic functions under boundary conditions, J. Math, and Phys. 46 (1967), 299–310.CrossRefGoogle Scholar