{"paper":{"title":"Matrix Riemann-Hilbert problems with jumps across Carleson contours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.CV","authors_text":"Jonatan Lenells","submitted_at":"2014-01-11T06:20:34Z","abstract_excerpt":"We develop a theory of $n \\times n$-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, 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 a vanishing lemma. We also investigate the implications of Fredholmness for the unique solvability and prove a theorem on contour deformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2506","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}