Polyanalytic boundary value problems for planar domains with harmonic Green function

Begehr H. Shupeyeva B.
September 2021 Birkhauser

Analysis and Mathematical Physics
2021 #11 Issue 3

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.

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

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Mathematisches Institut, FU Berlin, Arnimallee 3, Berlin, 14195, Germany
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