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Riemann-Hilbert problems

In: Application of Holomorphic Functions in Two and Higher Dimensions

Author

Listed:
  • Klaus Gürlebeck

    (Bauhaus-Universität Weimar)

  • Klaus Habetha

    (RWTH Aachen)

  • Wolfgang Sprößig

    (TU Bergakademie Freiberg)

Abstract

In his famous dissertation from 1851, Bernhard Riemann (1826–1866) formulated the following problem: In a given bounded domain of the complex plane, determine a holomorphic function, if a relation is prescribed between the boundary values of its real part and its imaginary part. In the case of a linear relation this problem was first considered in 1904 by David Hilbert (1862–1943). For this reason such problems are called Riemann-Hilbert problems. Sometimes also the term Hilbert problem is used.

Suggested Citation

  • Klaus Gürlebeck & Klaus Habetha & Wolfgang Sprößig, 2016. "Riemann-Hilbert problems," Springer Books, in: Application of Holomorphic Functions in Two and Higher Dimensions, chapter 0, pages 303-318, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0964-1_9
    DOI: 10.1007/978-3-0348-0964-1_9
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