Explicit solution of a class of Riemann-Hilbert problems

Darren Crowdy

Abstract


Analytical solutions to a special class of Riemann-Hilbert boundary value problems on multiply connected domains are presented. The solutions are written, up to a finite number of accessory parameters, as non-singular indefinite integrals whose integrands are expressed in terms of the Schottky-Klein prime function associated with the Schottky double of the planar domain.

Keywords


Riemann-Hilbert problem, boundary value problem, Schottky-Klein prime function

Mathematics Subject Classification


2000 Mathematics Subject Classification: 30C20, 30E25, 35F15

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