Riemann problem and singular integral equations with coefficients generated by piecewise constant functions
The paper deals with a class of Riemann boundary value problems with shift extending into the interior of the domain of interest. The coefficient functions are assumed to be piecewise constant. The results presented include sufficient conditions for the existence and uniqueness of the solution of the inhomogeneous problem and a method to find the dimension of the space of solutions of the homogeneous problem. The investigations make heavy use of Cauchy singular integral operators. Invertibility conditions for a class of such operators are discussed too.
scientific article; zbMATH DE number 5533519