The Riemann-Hilbert Problem and the Generalized Neumann Kernel on Un-Bounded Multiply Connected Regions

Abstract

A Fredholm integral equation of the second kind with the generalized  Neumann kernel associated with the Riemann-Hilbert problem on unbounded multiply connected regions will be derived and studied in this paper. The derived integral equation yields a uniquely solvable boundary integral equations for the modified Dirichlet problem on unbounded multiply connected regions.