2014•Complex Variables and Elliptic EquationsRequires access

A Riemann-Hilbert boundary value problem in a bounded sector

Mohamed S. Akel, Fatimah Alabbad

Abstract

In this article a Riemann-Hilbert boundary value problem in a bounded sector domain with angle is considered. A plane parqueting-reflection technique is used. Boundary behaviours of resulting integral operators are discussed in detail. Then we study the Riemann-Hilbert boundary value problem, with an arbitrary index, for both homogeneous and inhomogeneous Cauchy–Riemann equations. Expressions of solutions and the condition of solvability are explicitly obtained.

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Key concepts: Mathematics, Bounded function, Mathematical analysis, Boundary value problem, Boundary (topology), Riemann problem, Domain (mathematical analysis), Riemann–Hilbert problem