Polyanalytic boundary value problems for planar domains with harmonic Green function

There are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [u. Aksoy, H. Begehr, A.O. celebi, AV Bitsadze's observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257-1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

Automated summary

The paper investigates the boundary value problems for the inhomogeneous polyanalytic equation in planar domains, including the well-posed Schwarz problem, Dirichlet problem, and Neumann problem. While a modification is mentioned for the Schwarz problem, the Dirichlet problem is completely discussed for arbitrary order, and the Neumann problem is only handled for order up to three, with potential generalization to arbitrary order in the future.