Begehr, HeinrichShupeyeva, Bibinur2021-08-062021-08-062021-07-07Begehr, H., Shupeyeva, B. Polyanalytic boundary value problems for planar domains with harmonic Green function. Anal.Math.Phys. 11, 137 (2021). https://doi.org/10.1007/s13324-021-00569-21664-2368https://link.springer.com/article/10.1007%2Fs13324-021-00569-2https://doi.org/10.1007/s13324-021-00569-2http://nur.nu.edu.kz/handle/123456789/5661There 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesType of access: Open AccessAdmissible domainBi- and tri-analytic Pompeiu integral operatorsCauchy-Schwarz-Pompeiu representationDirichletGreen functionNeumann boundary value problemsPoly-analyticRing domainSchwarzArticle