JournalszaaVol. 27, No. 1pp. 53–66

On the Riemann–Hilbert Problem with a Piecewise Constant Matrix

  • Vladimir V. Mityushev

    Krakow Pedagogical Academy, Poland
  • Sergei V. Rogosin

    Belarusian State University, Minsk, Belarus
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Abstract

A constructive solution to the Riemann–Hilbert boundary value problem as well as to the C-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel–Schwarz transformation of the half-plane onto a circular polygon.

Cite this article

Vladimir V. Mityushev, Sergei V. Rogosin, On the Riemann–Hilbert Problem with a Piecewise Constant Matrix. Z. Anal. Anwend. 27 (2008), no. 1, pp. 53–66

DOI 10.4171/ZAA/1343