TY - JOUR
T1 - Polyanalytic boundary value problems for planar domains with harmonic Green function
AU - Begehr, Heinrich
AU - Shupeyeva, Bibinur
N1 - Funding Information:
Open Access funding enabled and organized by Projekt DEAL. The second named author was supported by Ministry of Education and Science of the Republic of Kazakhstan Grant No AP08052345 and in the fall term 2019 at FU Berlin through the Re-Invitation Programme for Former Scholarship Holders, 2019 (57440919) of the German Academic Exchange Service (DAAD).
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/9
Y1 - 2021/9
N2 - 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.
AB - 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.
KW - Admissible domain
KW - Bi- and tri-analytic Pompeiu integral operators
KW - Cauchy-Schwarz-Pompeiu representation
KW - Dirichlet
KW - Green function
KW - Neumann boundary value problems
KW - Poly-analytic
KW - Ring domain
KW - Schwarz
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U2 - 10.1007/s13324-021-00569-2
DO - 10.1007/s13324-021-00569-2
M3 - Article
AN - SCOPUS:85109705862
SN - 1664-2368
VL - 11
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 3
M1 - 137
ER -