The Generalized Riemann-Hilbert Boundary Value Problem for Non-Homogeneous Polyanalytic Differential Equation of Order $n$ in the Sobolev Space $W_{n,p}(D)$

Ali Seif Mshimba
1999 Zeitschrift für Analysis und ihre Anwendungen  
Given is a nonlinear non-homogeneous polyanalytic differential equation of order n in a simply-connected domain D in the complex plane. Initially we prove (under certain conditions) the existence of its general solution in W,(D) 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
more » ... rresponding one for a polyanalytic function. The latter is then transformed into n classical Riemann-Hilbert problems for holomorphic functions, whose solutions are known in the literature:
doi:10.4171/zaa/901 fatcat:bfbno3zfxjdtjgfbnend4dtx6a