JournalszaaVol. 20, No. 2pp. 513–524

The Generalized Riemann Problem of Linear Conjugation for Non-Homogeneous Polyanalytic Equations of Order nn in Wn,p(D)W_{n,p}(D)

  • Ali Seif Mshimba

    University of Dar es Salaam, Tanzania
The Generalized Riemann Problem of Linear Conjugation for Non-Homogeneous Polyanalytic Equations of Order $n$ in $W_{n,p}(D)$ cover
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Abstract

We consider a non-homogeneous polyanalytic partial differential equation of order nn in a simply-connected domain DD with smooth boundary D\partial D in the complex plane C\mathbb C. Initially we transform the given equation into an equivalent system of integro-differential equations and then find the general solution of the former in Wn,p(D)W_{n,p} (D). 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 nn classical Riemann problems of linear conjugation for nn 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.

Cite this article

Ali Seif Mshimba, The Generalized Riemann Problem of Linear Conjugation for Non-Homogeneous Polyanalytic Equations of Order nn in Wn,p(D)W_{n,p}(D). Z. Anal. Anwend. 20 (2001), no. 2, pp. 513–524

DOI 10.4171/ZAA/1028