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Mityushev, V. V., Rogosin, S. V. (2008). On the Riemann-Hilbert problem with a piecewise constant matrix. Zeitschrift f?r Analysis und ihre Anwendungen, 27 (1), 53-66.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.Peer reviewe

On the Riemann–Hilbert Problem with a Piecewise Constant Matrix