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 [Ü. Aksoy, H. Begehr, A.O. Çelebi, 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.

平面域中的非齐次多解析方程存在三个基本边值问题，一个是适定迭代 Schwarz 问题，还有两个 Dirichlet 和 Neumann 类型的超定迭代问题。在具有调和格林函数的平面域中研究这些问题。对于 Schwarz 问题，之前处理过 [Ü. Aksoy、H. Begehr、AO Çelebi、AV Bitsadze 对双分析函数和 Schwarz 问题的观察。Complex Var Elliptic Equ 64(8): 1257–1274 (2019)]，只是提到了一个修改。虽然 Dirichlet 问题完全讨论了任意阶次，但 Neumann 问题只处理了高达 3 阶的阶数。但是可能会泛化到任意顺序。