- Turkish Journal of Mathematics
- Vol: 42 Issue: 4
- Neumann boundary value problems in fan-shaped domains
Neumann boundary value problems in fan-shaped domains
Authors : Mohamed Akel, Mona Aldawsari
Pages : 1571-1589
View : 7 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
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