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On a class of systems of singular integral equations on a bounded domain

Published online by Cambridge University Press:  14 November 2011

A. Džuraev
A. Džuraev
Affiliation:
Tajik Academy of Sciences, Leninski Prospect 33, 734025 Dushanbe, U.S.S.R.
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Synopsis

A class of systems of two-dimensional singular integral equations with even kernels over bounded domains in the plane is studied. The applications include integral equations with the Bergman kernel function. The method of investigation is the following: the integral equation is reduced to a Riemann type boundary value problem for a first order elliptic system. This is solved by means of one-dimensional singular integral equations over the boundary curve. An adjoint problem is formulated, the Noetherian theorems are established, and a formula for the index is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 347 - 364
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Atkinson, F. V.. On relatively regular operators. Acta Sci. Math. (Szeged) 15 (1953), 38–56.Google Scholar
2Bergman, S.. The Kernel Function and Conformai Mapping (Providence, R. I.: Amer. Math. Soc, 1970).Google Scholar
3Bojarski, B.. Investigations of elliptic systems in the plane (Doctoral dissertation, Moscow, 1960) (Russian).Google Scholar
4Courant, R.. Dirichlet's Principle, Conformai Mapping and Minimal Surfaces (New York: Interscience, 1950).Google Scholar
5Džuraev, A.. The application of elliptic boundary value problems to the investigation of singular integral equations on bounded domain. Proceedings of symposium on continuum mechanics and related problems of analysis, Vol. II (Tbilissi, 1974).Google Scholar
6Džuraev, A.. On a method of investigating singular integral equations in a bounded plane region. Soviet Math. Dokl. 12/2 (1971), 653–657.Google Scholar
7Vekua, I. N.. Generalized analytic functions (London: Pergamon, 1962).Google Scholar
8Vinogradov, V. S.. The boundary-value problem for a first order elliptic system in the plane. Differential Equations 7/8 (1971), 1093–1099.Google Scholar
9Wendland, W.. Elliptic Systems in the Plane (London: Pitman, 1978).Google Scholar