Journal
MONATSHEFTE FUR MATHEMATIK
Volume 186, Issue 1, Pages 111-152Publisher
SPRINGER WIEN
DOI: 10.1007/s00605-017-1019-0
Keywords
Matrix Riemann-Hilbert problem; Cauchy integral; Carleson contour
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Funding
- EPSRC, UK
- European Research Council [682537]
- Swedish Research Council [2015-05430]
- Goran Gustafsson Foundation, Sweden
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We develop a theory of n x n-matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour Gamma is a finite union of simple closed Carleson curves in the Riemann sphere. In particular, unbounded contours with cusps, corners, and nontransversal intersections are allowed. We introduce a notion of L-p-Riemann-Hilbert problem and establish basic uniqueness results and Fredholm properties. We also investigate the implications of Fredholmness for the unique solvability and prove a theorem on contour deformation.
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