POLYANALYTIC BOUNDARY VALUE PROBLEMS FOR PLANAR DOMAINS WITH HARMONIC GREEN FUNCTION
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Date
2021-07-07
Authors
Begehr, Heinrich
Shupeyeva, Bibinur
Journal Title
Journal ISSN
Volume Title
Publisher
Birkhauser
Abstract
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.
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Keywords
Type of access: Open Access, Admissible domain, Bi- and tri-analytic Pompeiu integral operators, Cauchy-Schwarz-Pompeiu representation, Dirichlet, Green function, Neumann boundary value problems, Poly-analytic, Ring domain, Schwarz
Citation
Begehr, 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/s13324-021-00569-2