The Generalized Riemann-Hilbert Boundary Value Problem for Non-Homogeneous Polyanalytic Differential Equation of Order in the Sobolev Space
Ali Seif Mshimba
University of Dar es Salaam, Tanzania
![The Generalized Riemann-Hilbert Boundary Value Problem for Non-Homogeneous Polyanalytic Differential Equation of Order $n$ in the Sobolev Space $W_{n,p}(D)$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-18-issue-3.png&w=3840&q=90)
Abstract
Given is a nonlinear non-homogeneous polyanalytic differential equation of order in a simply-connected domain in the complex plane. Initially we prove (under certain conditions) the existence of its general solution in by first transforming it into a system of integro-differential equations. Next we prove the solvability of a generalized Riemann-Hilbert problem for the differential equation. This is effected by first reducing the boundary value problem posed to a corresponding one for a polyanalytic function. The latter is then transformed into classical Riemann-Hilbert problems for holomorphic functions, whose solutions are known in the literature.
Cite this article
Ali Seif Mshimba, The Generalized Riemann-Hilbert Boundary Value Problem for Non-Homogeneous Polyanalytic Differential Equation of Order in the Sobolev Space . Z. Anal. Anwend. 18 (1999), no. 3, pp. 611–624
DOI 10.4171/ZAA/901