A Boundary Integral Method for the General Conjugation Problem in Multiply Connected Circle Domains
We present a boundary integral method for solving a certain class of Riemann-Hilbert problems known as the general conjugation problem. The method is based on a uniquely solvable boundary integral equation with the generalized Neumann kernel. We present also an alternative proof for the existence and uniqueness of the solution of the general conjugation problem.
KeywordsGeneral conjugation problem Riemann-Hilbert problem Generalized Neumann kernel
Mathematics Subject Classification (2010)Primary 30E25; Secondary 45B05
The author would like to thank the anonymous referee for his valuable comments and suggestions which improved the presentation of this paper. The financial support from Qatar University Internal Grant QUUG-CAS-DMSP-15∖16-27 is gratefully acknowledged.
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