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On the theory of a singular Vekua system

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Problems and Methods in Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 121))

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Abstract

We study the solvability of the Riemann-Hilbert problem for a singular Vekua system. For the number of continuous solutions, we shall show that it depends not only on the index but also on the location and type of the singularities, moreover it does not depend continuously on the coefficients of the equation. These suggest essential difficulties to obtain a general theory for singular Vekua systems.

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References

  1. H. Begehr, Complex analytic methods for partial differential equations. An Introductory Text. World Scientific, Singapore etc., 1994.

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  2. H. Begehr & D. Q. Dai, On continuous solutions of a generalized Cauchy-Riemann system with more than one singularity, Preprint, 1999.

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  3. M. Reissig & A. Timofeev, Special Vekua equations with singular coefficients, Preprint, Bergakademie Freiburg, 1998.

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  4. A. Tungatarov, On the theory of Carleman-Vekua equation with a singular point, Russian Acad. Sci. Sb. Math. 78 (1994), 357–365.

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  5. A. Tungatarov, Continuous solutions of the generalized Cauchy-Riemann system with a finite number of singular points, Mat. Zametki 56 (1994), 105–115 (in Russian).

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  6. Z. D. Usmanov, Generalized Cauchy-Riemann systems with a singular point, Longman, Harlow, 1997.

    MATH  Google Scholar 

  7. I. N. Vekua, Generalized analytic functions, Pergamon, Oxford, 1962.

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  8. I. N. Vekua, On the class of elliptic systems with singularities, Proc. of the International Conference on Functional Analysis and Related Topics, Tokyo, April 1969.

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Author information

Authors and Affiliations

  1. I. Math. Institut, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    Heinrich Begehr

  2. Department of Mathematics, Zhongshan University, 510275, Guangzhou, China

    Dao-Qing Dai

Authors
  1. Heinrich Begehr
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  2. Dao-Qing Dai
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Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany

    Johannes Elschner

  2. Department of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    I. Gohberg

  3. Faculty of Mathematics, Technical University of Chemnitz, 09107, Chemnitz, Germany

    Bernd Silbermann

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© 2001 Springer Basel AG

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Begehr, H., Dai, DQ. (2001). On the theory of a singular Vekua system. In: Elschner, J., Gohberg, I., Silbermann, B. (eds) Problems and Methods in Mathematical Physics. Operator Theory: Advances and Applications, vol 121. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8276-7_4

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  • DOI: https://doi.org/10.1007/978-3-0348-8276-7_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9500-2

  • Online ISBN: 978-3-0348-8276-7

  • eBook Packages: Springer Book Archive

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