某类平面椭圆型一价偏微分方程组的Riemann-Hilbert边值问题——谨以本文纪念建校三十周年

On Riemann-Hilbert Boundary Value Probiem for a Kind of Eirst Order Elliptic Partial Differetial Equations iu the Plane

本文研究下列平面椭圆型方程的Riemann=Hilbert边值问题 这里,且复部丫0(z)≠0;G为单位圆盘,r:|z|=1,我们利用一类积分表达式,给出了问题的解的构造,将问题化为一个第二类Fredholm型分方程来求解。

In this paper, the Riemann - Hilbert boundary value problems for elliptic equations in the plane are consiered, where ∈ is a paramer; Akj , Bkj∈Lp (Ω), p<2; h(z)∈Lp(Ω); A(z)∈Hα(Γ and λ0(z)≠0;Ω is unit disk; Γ: |z|=1 By using integral representation formula, the solution of this problem is constructed We tranformed the problem into the Fredholm integral of second kind.