Riemann–Hilbert-type problems for the generalized Cauchy–Riemann equation with a leading coefficient having a singularity in a circle

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.