Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis
Reference34 articles.
1. Abdymanapov, S.A., Begehr, H., Tungatarov, A.B.: Some Schwarz problems in a quarter plane. Eurasian Math. J. 3, 22–35 (2005)
2. Abdymanapov, S.A., Begehr, H., Harutyunyan, G., Tungatarov, A.B.: Four boundary value problems for the Cauchy-Riemann equation in a quarter plane. In: More Progresses in Analysis, eds. H. Begehr et al., World Sci., Singapore, (2009), 1137–1147
3. Akel, M., Begehr, H.: Schwarz problem for first order elliptic systems in unbounded sectors. Eurasian Math. J. 5, 6–24 (2014)
4. Akel, M., Begehr, H.: Neumann function for a hyperbolic strip and a class of related plane domains. Math. Nachr. 290, 490–506 (2017). https://doi.org/10.1002/mana.201500501
5. Aksoy, Ü., Begehr, H., Çelebi, A.O.: Schwarz problem for higher-order complex partial differential equations in the upper half plane. Math. Nachr. 292, 1183–1193 (2019). https://doi.org/10.1002/mana.201800028
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献