Matrix Riemann-Hilbert problems with jumps across Carleson contours. (English) Zbl 1397.35163
The author discusses the matrix Riemann-Hilbert problems in the \(L_p\) space for a class of low regularity contours consisting of a finite number of the closed Carleson curves. The contours are allowed to pass through infinity and to have cusps, corners, and nontransversal intersections. The implications of Fredholmness for the unique solvability and contour deformation are investigated.
Reviewer: Vladimir Mityushev (Kraków)
MSC:
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 30E25 | Boundary value problems in the complex plane |
| 45E05 | Integral equations with kernels of Cauchy type |
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