Neumann boundary value problems in fan-shaped domains

Authors

MOHAMED AKEL
MONA ALDAWSARI

DOI

10.3906/mat-1604-83

Abstract

n this article we give the solvability conditions and the integral representations of the solutions of the Neumann boundary value problem for the Cauchy-Riemann operator and the Beltrami operator with constant coefficient in a disc sector with angle $\vartheta=\frac{\pi}{n},\,n\in\mathbb N$. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part is studied. Classical results of complex analysis are used to obtain the expressions of the solvability conditions and the integral representations for the solutions explicitly.

Keywords

Cauchy-Riemann equation, Beltrami equation, Bitsadze/Poisson equation, Neumann problem, Neumann series method

First Page

1571

Last Page

1589

Recommended Citation

AKEL, MOHAMED and ALDAWSARI, MONA (2018) "Neumann boundary value problems in fan-shaped domains," Turkish Journal of Mathematics: Vol. 42: No. 4, Article 4. https://doi.org/10.3906/mat-1604-83
Available at: https://journals.tubitak.gov.tr/math/vol42/iss4/4