Abstract: The Riemann-Hilbert problem for first order linear elliptic complex equation with parabolic degeneracy is dealed with here. Firstly, the formulation and representation of solutions of the above boundary value problem are given, and then the existence and uniqueness of solutions for the above problem are proved, in which the complex analytic method is used.

Key words: Riemann-Hilbert problem, degenerate elliptic complex equations of first order

摘要： 讨论了一阶退化椭圆型复方程的Riemann-Hilbert边值问题。先给出这种边值问题的提法和解的表示式，然后使用复分析方法证明了上述边值问题解的存在性和唯一性。

关键词: Riemann-Hilbert边值问题, 一阶退化椭圆型复方程