Functional Equations in Mathematical Analysis

Volume 52 of the series Springer Optimization and Its Applications pp 599-632


Scalar Riemann–Hilbert Problem for Multiply Connected Domains

  • Vladimir V. MityushevAffiliated withDepartment of Computer Science and Computer Methods, Pedagogical University Email author 

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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.


Boundary value problem Multiply connected domain Schwartz operator Poincaré series Dirichlet problem Harmonic measure Green function