边界条件中带较弱系数的Riemann-Hilbert边值问题

Riemann-Hilbert Boundary Value Problems with Weaker Coefficients in the Boundary Condition

主要目的是讨论一阶非线性椭圆型复方程在边界条件中带有较弱系数的Riemann-Hilbert边值问题。为此,我们先提出相应于问题A的变态边值问题B,并给出解析函数问题B与问题A的解,然后利用复方程的解的表示式与先验估计以及Schauder不动点定理证明复方程问题B的可解性,从而导出复方程问题A的可解性结果。

The main purpose of this paper is to discuss Riemann Hilbert boundary value problems (Problem A) with weaker coefficients in the boundary condition for nonlinear elliptic complex equation of first order. For this sake, the authors first propose a modifiedboundary value problems (Problem B) corresponding to Problem A, and give solutions of both Problem B and Problem A for analytic function, and then prove the solvability of Problem B for complex equation by using the expression together with prior estimates of solutions for complex equation as well as Schauder fixpoint theorem. Thus the results on solvability for Problem A of the complex equation is derived.