On the Riemann-Hilbert boundary value problem for generalized analytic functions in the framework of variable exponent spaces

2017 ◽  
Vol 40 (18) ◽  
pp. 7267-7286 ◽  
Author(s):  
V. Kokilashvili ◽  
V. Paatashvili
Keyword(s):  
Boundary Value Problem ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Boundary Value ◽  
Generalized Analytic Functions ◽  
Variable Exponent Spaces ◽  
Hilbert Boundary Value Problem

scholarly journals Hilbert boundary value problem for generalized analytic functions with a singular line

2021 ◽  
Vol 274 ◽  
pp. 11003
Author(s):  
Pavel Shabalin ◽  
Rafael Faizov
Keyword(s):  
Boundary Value Problem ◽  
Analytic Functions ◽  
Boundary Value ◽  
Singular Line ◽  
Infinite Index ◽  
Number Of Solutions ◽  
Singular Coefficient ◽  
Generalized Analytic Functions ◽  
Complete Study ◽  
Hilbert Boundary Value Problem

In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and a boundary condition on a circle for a generalized Cauchy-Riemann equation with a singular coefficient. To solve this problem, we conducted a complete study of the solvability of the Hilbert boundary value problem of the theory of analytic functions with an infinite index due to a finite number of points of a special type of vorticity. Based on these results, we have derived a formula for the general solution and studied the existence and number of solutions to the boundary value problem of the theory of generalized analytic functions.

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