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Nonlinear Riemann–Hilbert problems with Lipschitz-continuous boundary data without transversality

✍ Scribed by M.A. Efendiev; W.L. Wendland

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
362 KB
Volume
47
Category
Article
ISSN
0362-546X

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✦ Synopsis

Here we consider holomorphic functions in a given circular annulus which satisfy nonlinear boundary conditions on the two circles of the boundary. In order to handle global solvability we introduce an additional real parameter. For large moduli of the desired solution, the boundary conditions are supposed to become linear RiemannHilbert conditions. Solvability of the problem is proved by applying the topological degree theory of quasilinear Fredholm mappings to an equivalent system of nonlinear Cauchy singular integral equations.

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