The Riemann–Hilbert problem is a classical problem in mathematics that arises in the context of complex analysis, mathematical physics, and the theory of differential equations. The problem involves finding a complex function that satisfies specific analytic properties while also meeting certain boundary conditions.
Articles by others on the same topic
Find functions analytic on the two sides of a contour whose boundary values obey a prescribed jump, with suitable normalization at infinity and other distinguished points. An additive jump on a counterclockwise closed contour is solved by the Cauchy integral formula , subject to the normalization and compatibility conditions. The Sokhotski–Plemelj theorem verifies the jump.