A nonlinear boundary problem
Author:
John R. Hatcher
Journal:
Proc. Amer. Math. Soc. 95 (1985), 441-448
MSC:
Primary 30E25; Secondary 45E10
DOI:
https://doi.org/10.1090/S0002-9939-1985-0806084-2
MathSciNet review:
806084
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Abstract | References | Similar Articles | Additional Information
Abstract: A nonlinear Hilbert problem of power type is solved in closed form by representing a sectionally holomorphic function by means of an integral with power kernel. This technique transforms the problem to one of solving an integral equation of the generalized Abel type.
- [1] K. D. Sakalyuk, Abel’s generalized integral equation, Soviet Math. Dokl. 1 (1960), 332–335. MR 0117520
- [2] N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR 0355494
- [3] Norman Levinson, Simplified treatment of integrals of Cauchy type, the Hilbert problem and singular integral equations. Appendix: Poincaré-Bertrand formula, SIAM Rev. 7 (1965), 474–502. MR 185398, https://doi.org/10.1137/1007105
- [4] Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition. Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1985-0806084-2
Keywords:
Cauchy integral,
Plemelj formulae,
nonhomogeneous boundary value problem
Article copyright:
© Copyright 1985
American Mathematical Society
