关于双特征Beltrami方程

该文研究空间Ｂｅｌｔｒａｍｉ方程的推广形式，即双特征Ｂｅｌｔｒａｍｉ方程．利用外微分形式与矩阵的外代数等工具，将双特征Ｂｅｌｔｒａｍｉ方程转化为一个非齐次的狆 调和方程，转化过程中只用到加于特征矩阵的一致椭圆型条件．然后验证了算子犃满足的条件：Ｌｉｐｓｃｈｉｔｚ型条件、单调不等式、齐次性条件以及算子犅满足的控制增长条件．并利用得到的狆 调和方程，给出了双特征Ｂｅｌｔｒａｍｉ方程广义解分量函数的弱单调性结果．

On Beltrami Equation With Double Characteristic Matrices

This paper considers Beltrami equation with double characteristic matrices which can be regarded as the generalized form of Beltrami equation. By using the outer differential forms and the outer algebra of matrices, we deform the Beltrami equation with double characteristic matrices to a nonhomogeneous p-harmonic equation, in which we only use the uniform elliptic condition of the characteristic matrices. Then, we derive the conditions of the operator A: the Lipschitz type condition, the monotonicity inequality, the homogenity condition, and the controlled increasing condition of the operator B. Finally, we use the p-harmonic equation to derive the weakly monotonicity result of the component function of the generalized solutins of double characteristic matrices.