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June 2009 Nonlinear Riemann-Hilbert Problems for Generalized Analytic Functions
Messoud A. Efendiev, Wolfgang L. Wendland
Funct. Approx. Comment. Math. 40(2): 185-208 (June 2009). DOI: 10.7169/facm/1246454028


In this study we deal with the nonlinear Riemann--Hilbert problem (in short (RHP)) for generalized analytic functions in multiply connected domains. Using a similarity principle for multiply connected domains (presented here for the first time), we reduce the nonlinear RHP for generalized analytic functions to a corresponding nonlinear RHP for holomorphic functions with Hölder continuous boundary data. Then the Newton--Kantorovič method combined with a continuation procedure as well as a new existence theorem for holomorphic solutions, which is based on topological degree arguments, leads to existence of at least two topologically different generalized analytic functions solving the nonlinear RHP.


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Messoud A. Efendiev. Wolfgang L. Wendland. "Nonlinear Riemann-Hilbert Problems for Generalized Analytic Functions." Funct. Approx. Comment. Math. 40 (2) 185 - 208, June 2009.


Published: June 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1192.30010
MathSciNet: MR2543556
Digital Object Identifier: 10.7169/facm/1246454028

Primary: 30G20
Secondary: 35J65, 45G05, 47H11

Rights: Copyright © 2009 Adam Mickiewicz University


Vol.40 • No. 2 • June 2009
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