Schwarz boundary value problem in half lens and half lune. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Taghizadeh, N.; Soltani Mohammadi, V.; Najand Foumani, M.
• Is Part Of: Complex variables and elliptic equations. Volume 61:Issue 4(2016)
• Page Start: 484
• Page End: 495
• Publication Date: 2016-04-02
• Subjects: Schwarz problem -- Cauchy-Pompeiu formula -- Cauchy–Schwarz representation -- half lens -- half lune; 35F15 -- 30E25 -- 35C15; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2015.1101076
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : In this article, firstly we obtain Cauchy–Schwarz representation in a half lens in . Then, we consider the Schwarz boundary value problem for the inhomogeneous Cauchy–Riemann equation and explicit expression of solution is obtained. Secondly, the Schwarz problem is explicitly solved in two half lunes which are complements of the half lens with respect to two orthogonal half circles.