Abstract: Though the general discontinuous Riemann-Hilbert problem for analytic functions in simply connected domains was solved, the general discontinuous Riemann-Hilbert problem for analytic functions in multiply connected domains has not been completely solved. The author proposes a well posed-ness of general discontinous Riemann-Hilbert problem for analytic functions, and proves the uniqueness and existence of solutions for the problem.

Key words: discontinuous Riemann-Hilbert problems, analytic functions, multiply connected domains

摘要： 针对解析函数在多连通区域上的间断边值问题没有得完全的解决, 提出完整解决解析函数在多连通区域上的间断Riemann-Hilbert边值问题的方法, 并给出此间断边值问题的适定提法, 证明了该间断边值问题解的存在唯一性。

关键词: 间断Riemann-Hilbert问题, 解析函数, 多连通区域