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Scalar Riemann–Hilbert Problem for Multiply Connected Domains

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Vladimir V. Mityushev

    (Pedagogical University)

Abstract

We solve the scalar Riemann–Hilbert problem for circular multiply connected domains. The method is based on the reduction of the boundary value problem to a system of functional equations (without integral terms). In the previous works, the Riemann–Hilbert problem and its partial cases such as the Dirichlet problem were solved under geometrical restrictions to the domains. In the present work, the solution is constructed for any circular multiply connected domain in the form of modified Poincaré series.

Suggested Citation

  • Vladimir V. Mityushev, 2011. "Scalar Riemann–Hilbert Problem for Multiply Connected Domains," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 599-632, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_38
    DOI: 10.1007/978-1-4614-0055-4_38
    as

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