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Riemann boundary value problem with square roots on an open arc

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Wuhan University Journal of Natural Sciences

Abstract

The Riemann boundary value problem with square roots in class h 0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω(z) is introduced. With different choices of ω(z)’s, some interesting examples are illustrated.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China

    Chen Jingsong & Lu Jianke

  2. School of Information, Zhongnan University of Economics and Law, Wuhan, 430073, Hubei, China

    Chen Jingsong

Authors
  1. Chen Jingsong
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  2. Lu Jianke
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Additional information

Foundation item: Supported by the National Natural Science Foundation of China (10161009)

Biography: CHEN Jingsong(1979-), male, Ph. D. candidate, Lecturer of Zhongnan University of Economics and Law, research direction: complex analysis.

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Chen, J., Lu, J. Riemann boundary value problem with square roots on an open arc. Wuhan Univ. J. of Nat. Sci. 12, 193–197 (2007). https://doi.org/10.1007/s11859-006-0003-7

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  • DOI: https://doi.org/10.1007/s11859-006-0003-7

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