The Hilbert boundary value problem for analytic functions on multiply connected domains

1992 ◽  
pp. 189-230
Keyword(s):  
Boundary Value Problem ◽  
Analytic Functions ◽  
Boundary Value ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
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.

On the Hilbert boundary-value problem for Beltrami equations with singularities

2021 ◽  
Author(s):  
Vladimir Gutlyanskiĭ ◽  
Vladimir Ryazanov ◽  
Eduard Yakubov ◽  
Artyem Yefimushkin
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Beltrami Equations ◽  
Hilbert Boundary Value Problem

Optimal Solutions for Nonhomogeneous Multiply-Connected Torsional Sections

1989 ◽  
Vol 111 (1) ◽  
pp. 87-93 ◽  
Author(s):  
A. Mioduchowski ◽  
M. G. Faulkner ◽  
B. Kim
Keyword(s):  
Numerical Simulation ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Boundary Value ◽  
Optimization Procedure ◽  
Second Order ◽  
External Boundary ◽  
Optimal Solutions ◽  
Torsion Problem ◽  
Multiply Connected

Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.

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