一阶,二阶线性混合型复方程的一些边值问题

只讨论最简单的一阶混合型（椭圆－双曲型）复方程（方程组的复形式）与二阶混合型（椭圆－双曲型）方程。首先，我们证明一阶混合型复方程Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题解的唯一性，然后使用关于解析函数间断Ｒｉｅｍａｎｎ－Ｈｉｂｅｒｔ边值问题的结果证明上述边值问题的存在性，进而又用一阶混合型方程的上述结果导出二阶混合型方程斜微商边值问题的可解性。Ａ．Ｖ．Ｂｉｃａｄｚｅ用复分析方法证明了二阶混合型Ｄｉｒ

Some Boundary Value Problems for Linear Mixed Complex Equations of First and Second Order

This paper deals with the Riemann Hilbert boundary value problem for mixed(elliptic hyperbolic) complex equation of first order and the oblique derivative problem for mixed equation of seond order in a simply connected domain. The uniqueness theorems of solutions for above boundary value problems are given, afterwards by using the method of complex analysis, the existence of solutions for the above problems is proved. A.V.Bicadze discussed the Dirichlet boundary value problem for the mixed equation of second order, in the present paper by using the result on discontinuous Riemann Hilbert problem for analytic functions the above results on the Riemann Hilbert problem for mixed complex equation of first order and the oblique derivative problem for the mixed equation of second order are deried. The results in this paper include some results obtained by A.V.Bicadze as special cases.