We consider a non-homogeneous polyanalytic partial differential equation of order in a simply-connected domain with smooth boundary in the complex plane . Initially we transform the given equation into an equivalent system of integro-differential equations and then find the general solution of the former in . Next we pose and prove the solvability of a generalized Riemann problem of linear conjugation to the differential equation. This is effected by first reducing the Riemann problem to a corresponding one for a polyanalytic function. The latter is solved by first transforming it into classical Riemann problems of linear conjugation for holomorphic functions expressed in terms of the analytic functions which define the polyanalytic function. The solution of the classical Riemann problem is available in the literature.
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Ali Seif Mshimba, The Generalized Riemann Problem of Linear Conjugation for Non-Homogeneous Polyanalytic Equations of Order in . Z. Anal. Anwend. 20 (2001), no. 2, pp. 513–524DOI 10.4171/ZAA/1028