关于二阶常系数线性椭圆型偏微分方程组解的唯一性的若干结论

Some Results in the Uniqueness of Solution about Linear Elliptical Partical Difference Equations of Two order

本文证明了一个矩阵方面的有用结论，即文中定理２，说明了当条件（Ⅰ）、（Ⅱ）成立时，对于二个自变量、二个未知函数的二阶常系数线性方程组（１）可化为强椭圆型方程组，这一结论也可推广到某些三个未知函数的情形。利用强椭圆型方程组解必定唯一的结论，证明了某些二阶常系数线性椭圆型方程组在有界闭区域内Ｄｉｒｉｃｈｌｅｔ问题解的唯一性。

This paper gives an useful result about rectangles, i.e. the result of Th.2. And it shows that the two order constant coefficient equations (1) for two independent variables, two unknown functions can be transformed into strongly elliptical difference equations. And this resultcan also be extended to the case of some three unknown functions. By use of the result that the strongly elliptical equations has the uniqueness of the solution, it is proved that the uniqueness of the solution about the Dirichlet problem for some linear elliptical partial difference equations of two order in a bounded domain.