Abstract:
In this work, we construct a general solution of the generalized Cauchy-–Riemann equation
whose coefficient admits a first-order singularity on a circle contained in the domain, and study
a boundary-value problem that combines elements of the Riemann-–Hilbert problem and the linear
conjugation problem.
Keywords:Cauchy–Riemann equations, singularity in the coefficient, Pompeiu–Vekua operator, boundary-value problem