Polyanalytic boundary value problems for planar domains with harmonic Green function
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AbstractThere 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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1981 ◽
Vol 81
(1)
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pp. 99-133
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1989 ◽
Vol 12
(8)
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pp. 959-966
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2012 ◽
Vol 3
(4)
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pp. 421-472