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A Boundary Integral Method for the General Conjugation Problem in Multiply Connected Circle Domains

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Modern Problems in Applied Analysis

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We present a boundary integral method for solving a certain class of Riemann-Hilbert problems known as the general conjugation problem. The method is based on a uniquely solvable boundary integral equation with the generalized Neumann kernel. We present also an alternative proof for the existence and uniqueness of the solution of the general conjugation problem.

This paper has been presented in: BFA 3rd meeting, Rzeszow, Poland, April 20–23, 2016. The author is grateful to Qatar University for the financial support to attend the meeting and to professor Piotr Drygas, chairman of the organizing committee of the meeting, for the hospitality during the meeting.

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Acknowledgements

The author would like to thank the anonymous referee for his valuable comments and suggestions which improved the presentation of this paper. The financial support from Qatar University Internal Grant QUUG-CAS-DMSP-15∖16-27 is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Physics, Qatar University, P.O. Box 2713, Doha, Qatar

    Mohamed M. S. Nasser

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  1. Mohamed M. S. Nasser
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Correspondence to Mohamed M. S. Nasser .

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Editors and Affiliations

  1. Department of Mathematics & Natural Sciences, Rzeszow University, Rzeszów, Poland

    Piotr Drygaś

  2. Department of Economics, Belarusian State University, Minsk, Belarus

    Sergei Rogosin

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Nasser, M.M.S. (2018). A Boundary Integral Method for the General Conjugation Problem in Multiply Connected Circle Domains. In: Drygaś, P., Rogosin, S. (eds) Modern Problems in Applied Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-72640-3_11

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