On the Riemann–Hilbert Problem with a Piecewise Constant Matrix

Abstract

The vector-matrix Riemann boundary value problem for the unit disk with piecewise constant matrix is constructively solved by a method of functional equations. By functional equations we mean iterative functional equations with shifts involving compositions of unknown functions analytic in mutually disjoint disks. The functional equations are written as an infinite linear algebraic system on the coefficients of the corresponding Taylor series. The compactness of the shift operators implies justification of the truncation method for this infinite system. The unknown functions and partial indices can be calculated by truncated systems.

Effective anti-plane properties of piezoelectric fibrous composites

“…The problem (103) was not investigated in [34,37,44]. However, the result [46] suggests that the R-linear vector-matrix problem (103) can be solved by similar methods.…”