LAUSR

We develop a theory of $$n \times n$$n×n-matrix Riemann–Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour $$\Gamma $$Γ 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 $$L^p$$Lp-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.