The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem

2001 ◽  
pp. 315-330
Author(s):  
Raghavan Narasimhan ◽  
Yves Nievergelt
Keyword(s):  
Riemann Equation ◽  
Cauchy Riemann

SOME BOUNDARY VALUE PROBLEMS FOR THE CAUCHY-RIEMANN EQUATION IN HALF LENS

2018 ◽  
Vol 9 (3) ◽  
pp. 73-84
Author(s):  
N. Taghizadeh ◽  
◽  
V. Soltani Mohammadi ◽  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Riemann Equation ◽  
Cauchy Riemann

Hilbert Problem for the Cauchy–Riemann Equation with a Singular Circle and a Singular Point

2019 ◽  
Vol 241 (3) ◽  
pp. 327-339
Author(s):  
A. B. Rasulov ◽  
M. A. Bobodzhanova ◽  
Yu. S. Fedorov
Keyword(s):  
Singular Point ◽  
Hilbert Problem ◽  
Riemann Equation ◽  
Cauchy Riemann

Solutions of the Riemann–Hilbert–Poincaré problem and the Robin problem for the inhomogeneous Cauchy–Riemann equation

2009 ◽  
Vol 139 (1) ◽  
pp. 157-181 ◽  
Author(s):  
Alip Mohammed ◽  
M. W. Wong
Keyword(s):  
Boundary Condition ◽  
Linear Equations ◽  
Robin Boundary Condition ◽  
Robin Problem ◽  
System Of Linear Equations ◽  
Riemann Equation ◽  
Cauchy Riemann ◽  
Robin Boundary ◽  
Poincaré Problem ◽  
Well Posed

The Riemann–Hilbert–Poincaré problem with general coefficient for the inhomogeneous Cauchy–Riemann equation on the unit disc is studied using Fourier analysis. It is shown that the problem is well posed only if the coeffcient is holomorphic. If the coefficient has a pole, then the problem is transformed into a system of linear equations and a finite number of boundary conditions are imposed in order to find a unique and explicit solution. In the case when the coefficient has an essential singularity, it is shown that the problem is well posed only for the Robin boundary condition.

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