2995-3162ISSN (Online)
Volume 2 , Issue 2 , PP: 23-29, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Rashel Abu Hakmeh 1 *
Doi: https://doi.org/10.54216/PMTCS.020202
In this paper, we find the formula of Cauchy – Pompeiu's integral in the octal of unit disk of the complex plain, by using the reflection method to determine the Integral's Cauchy – Pompeiu's operator. Also, we give many related examples about the novel formula.
Cauchy &ndash , Pompeiu's integral , reflection , Cauchy &ndash , Pompeiu's operator
[1] H.Begehr, T.Vaitekhovich, Harmonic boundary value problems in half disc and half ring, Functiones et Approximatio, 40.2,(2009), pp.251-282.
[2] B. Shupeyeva, “Harmonic boundary value problems in a quarter ring domain”, Advances in Pure and Applied Mathematics, vol.3, no. 4, pp. 393–419, (2012).
[3] B.Shupeyeva, Dirichlet Problem for Complex Poisson Equation in a Half Hexagon Domain, Journal of Complex Analysis,(2016).
[4] H. Begehr, S.Burgumbayeva, B.Shupeyeva, Harmonic Green Functions for a Plane Domain With two Touching Circles as Boundary, Advanced Mathematical Models & Applications, vol.3, no.1, pp. 18–29, (2018).
[5] Y. Wang, Boundary value problems for complex partial differential equations in fanshaped domains, Ph.D. thesis, FU Berlin, (2011), ttp://www.diss.fuberlin.de/diss/receive.FUDISS-thesis-000000021359.
[6] B.Shupeyeva, Some Basic Boundary Value Problems for Complex Partial Differential Equations in Quarter Ring and Half Hexagon, Ph.D. thesis, FU Berlin,(2013).
[7] T.Vaitsiakhovich, Boundary Value Problems for Complex Partial Differential Equations in a ring domain, PhD thesis, FU Berlin, 2008; www.diss.fu-berlin.de/diss/receive/FUDISS thesis 000000003859.
[8] H.Begehr, , T.Vaitekhovich, Schwarz problem in lens and lune. Complex Var. Ell. Eq., 59(1), 76–84 (2014).
