## Abstract The paper gives a systematic and self‐contained treatment of the nonlinear Riemann–Hilbert problem with circular target curves |__w__ – __c__ | = __r__, sometimes also called the generalized modulus problem. We assume that __c__ and __r__ are Hölder continuous functions on the unit circ
Nonlinear Riemann-Hilbert Problems with Unbounded Restriction Curves
✍ Scribed by Elias Wegert
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 310 KB
- Volume
- 170
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Using a norm inequality for singular integral operators in pairs of weighted Lebesgue spaces we prove new existence and uniqueness results for solutions of nonlinear Riemann‐Hilbert problems with noncompact restriction curves.
📜 SIMILAR VOLUMES
## Abstract For holomorphic functions in the unit disc, we consider a general nonlinear boundary condition whose linearisation admits jump discontinuities at a finite number of points on the unit circle, the boundary of the unit disc. By using the properties of quasilinear Fredholm maps of the corr
where ~( 5 ) is a rational function. ## Bibliography [I] Pogorzelski, W., Integral Equations and their Applications, Pergamon Press, 1966, (see the references [2] Peters, A. S., Pairs o f Cauchy singular integral equations and the kernel [ b ( z ) f a ( { ) ] / ( z -{), at the end of this book).
## Abstract This paper concerns the existence of nontrivial solutions of the Riemann‐Hilbert problem with a continuous coefficient whose values belong to two rays in the complex plane. Our results extend those recently obtained by E. Shargorodsky and J. F. Toland [6]. (© 2004 WILEY‐VCH Verlag GmbH