Anoverview of complex boundary value problems

Okay Çelebi

doi:10.26650/ijmath.2025.00025

Anoverview of complex boundary value problems

Abstract

In this overview we have pointed out some boundary value problems in a subset of complex plane. We start with Cauchy-Riemann operator and their conjugates. Then we introduce the Cauchy- Riemann operator and its conjugate. Firstly, we introduce the polyanalytic Pompeiu integral representation 𝑇 𝑓 and its conjugate which vanish at infinity. The basic polyanalytic Schwarz and polyanalytic Dirichlet problems are introduced. The later part is devoted to polyanalytic problems and discussions on polyharmonic problems. We have also summarized polyanalytic Neumann problem in the unit disk for 𝜕𝑧𝑤 = 𝑓. In this case, we may have three types of boundaryvalueproblems.ThosearepolyharmonicDirichletproblem,polyharmonicNeumannproblemandpolyharmonic Riquier (Navier) problem. In this later part we have given the iterated polyharmonic Green function.

Keywords

References

Aksoy, Ü., Begehr, H., Çelebi, A., Shupeyeva, B., 2025, Complex partial differential equations, Journal of Mathematical Sciences, Vol. 287, No. 6. google scholar
Begehr, H., 2025, Polyanalytic Neumann-n problem in the unit disk, Complex Variables and Elliptic Equations, 70:2, 278-286. google scholar
Vekua, I.N., 1962, Generalized Analytic Functions, Pergamon Press, Oxford. google scholar

Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Okay Çelebi ^*
Türkiye

Publication Date

June 24, 2025

Submission Date

May 16, 2025

Acceptance Date

June 19, 2025

Published in Issue

Year 2025 Volume: 3 Number: 1

DOI

https://doi.org/10.26650/ijmath.2025.00025

IZ

https://izlik.org/JA63YA69YK

Cite

RIS / Bibtex

APA

Çelebi, O. (2025). Anoverview of complex boundary value problems. Istanbul Journal of Mathematics, 3(1), 39-44. https://doi.org/10.26650/ijmath.2025.00025

AMA

1.Çelebi O. Anoverview of complex boundary value problems. Istanbul Journal of Mathematics. 2025;3(1):39-44. doi:10.26650/ijmath.2025.00025

Chicago

Çelebi, Okay. 2025. “Anoverview of Complex Boundary Value Problems”. Istanbul Journal of Mathematics 3 (1): 39-44. https://doi.org/10.26650/ijmath.2025.00025.

EndNote

Çelebi O (June 1, 2025) Anoverview of complex boundary value problems. Istanbul Journal of Mathematics 3 1 39–44.

IEEE

[1]O. Çelebi, “Anoverview of complex boundary value problems”, Istanbul Journal of Mathematics, vol. 3, no. 1, pp. 39–44, June 2025, doi: 10.26650/ijmath.2025.00025.

ISNAD

Çelebi, Okay. “Anoverview of Complex Boundary Value Problems”. Istanbul Journal of Mathematics 3/1 (June 1, 2025): 39-44. https://doi.org/10.26650/ijmath.2025.00025.

JAMA

1.Çelebi O. Anoverview of complex boundary value problems. Istanbul Journal of Mathematics. 2025;3:39–44.

MLA

Çelebi, Okay. “Anoverview of Complex Boundary Value Problems”. Istanbul Journal of Mathematics, vol. 3, no. 1, June 2025, pp. 39-44, doi:10.26650/ijmath.2025.00025.

Vancouver

1.Okay Çelebi. Anoverview of complex boundary value problems. Istanbul Journal of Mathematics. 2025 Jun. 1;3(1):39-44. doi:10.26650/ijmath.2025.00025