The Generalized Riemann Problem of Linear Conjugation for Polyanalytic Functions of Order $n$ in $W_{n,p}(D)$

Abstract

We consider a homogeneous polyanalytic differential equation of order $n$ in a simply-connected domain $D$ with a smooth boundary $\partial D$ in the complex plane $\mathbb C$. We pose and then prove solvability of a generalized Riemann problem of linear conjugation to the differential equation. This is done by reducing the problem into $n$ classical Riemann problems of linear conjugation for holomorphic functions, the solution of which is available in the literature.