ON THE RIEMANN-HILBERT PROBLEM FOR FIRST ORDER ELLIPTIC SYSTEMS IN MULTIPLY CONNECTED DOMAINS

1995 ◽  
Vol 80 (2) ◽  
pp. 287-307 ◽  
Author(s):  
M M Sirazhudinov
Keyword(s):  
Hilbert Problem ◽  
Elliptic Systems ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
First Order ◽  
Riemann Hilbert Problem

scholarly journals On the Riemann-Hilbert problem in multiply connected domains

2016 ◽  
Vol 14 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Vladimir Ryazanov
Keyword(s):  
Boundary Data ◽  
Hilbert Problem ◽  
Multiply Connected Domains ◽  
Natural Parameter ◽  
Multiply Connected ◽  
Jordan Curves ◽  
Measurable Coefficients ◽  
Asymptotic Values ◽  
Riemann Hilbert Problem ◽  
Number Of Branches

AbstractWe proved the existence of multivalent solutions with the infinite number of branches for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The theorem is formulated in terms of harmonic measure and principal asymptotic values. It is also given the corresponding reinforced criterion for domains with rectifiable boundaries stated in terms of the natural parameter and nontangential limits. Furthermore, it is shown that the dimension of the spaces of these solutions is infinite.

On the asymptotics of meromorphic solutions for nonlinear Riemann–Hilbert problems

1999 ◽  
Vol 127 (1) ◽  
pp. 159-172 ◽  
Author(s):  
H. BEGEHR ◽  
M. A. EFENDIEV
Keyword(s):  
Hilbert Problem ◽  
Singular Part ◽  
Regular Part ◽  
Multiply Connected Domains ◽  
Winding Number ◽  
Meromorphic Solutions ◽  
Holomorphic Solution ◽  
Multiply Connected ◽  
Global Existence Theorem ◽  
Riemann Hilbert Problem

This paper is devoted to a global existence theorem of meromorphic solutions of the form Z(z)=Zo(z)+R(z) of a nonlinear Riemann–Hilbert problem (RHP) for multiply connected domains Gq(q[ges ]1), where Zo(z) is the singular part of the solution, R(z) is the regular part which is a holomorphic solution of some appropriate nonlinear RHP for Gq(q[ges ]1). Under appropriate conditions on the characteristics of both the singular part Zo(z) (number of poles) and regular part (winding number) we prove the existence of meromorphic solutions Z(z) of the form Z(z)=Zo(z)+R(z). The proof is based on a special construction of the singular part Zo(z) and an adequate formulation of Newton's method for the regular part R(z).

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