Nonlinear Riemann-Hilbert problems for doubly connected domains and closed boundary data

M. A. Efendiev, W. L. Wendland

DOI: http://dx.doi.org/10.12775/TMNA.2001.007

Abstract


In this paper, for nonlinear Riemann–Hilbert problems in doubly
connected domains with smooth as well as Lipschitz continuous boundary
data, existence of at least two topologically different solutions is established.
The main tools are the topological degree of quasi-ruled Fredholm
mappings, Montel’s theorem, a priori estimates and the employment of
classical modular function theory.

Keywords


Universal covering theorem; modular functions; topological degree; fundamental group; nonlinear Riemann-Hilbert problems

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