Lenells Jonatan
Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden.
Mon Hefte Math. 2018;186(1):111-152. doi: 10.1007/s00605-017-1019-0. Epub 2017 Jan 28.
We develop a theory of -matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour 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 -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.
我们针对一类具有低正则性的跳跃轮廓和跳跃矩阵，发展了一种关于(\Psi)-矩阵黎曼 - 希尔伯特问题的理论。我们的基本假设是，轮廓(\Gamma)是黎曼球面上简单闭卡尔松曲线的有限并集。特别地，允许具有尖点、角点和非横向交点的无界轮廓。我们引入了(\Psi)-黎曼 - 希尔伯特问题的概念，并建立了基本的唯一性结果和弗雷德霍姆性质。我们还研究了弗雷德霍姆性对唯一可解性的影响，并证明了一个关于轮廓变形的定理。
