关于双特征Beltrami方程  

On Beltrami Equation With Double Characteristic Matrices

作　　者：高红亚[1] 吴泽民[2] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002 [2]上海交通大学应用数学系

出　　处：《数学物理学报（A辑）》2002年第4期433-440,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金 (1 95 3 1 0 60 );国家教育部博士点基金 (970 2 4 81 1 );河北大学博士科研启动基金资助项目

摘　　要：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 p-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 A满足的条件 :Lipschitz型条件、单调不等式、齐次性条件以及算子 B满足的控制增长条件 .并利用得到的 p-调和方程 ,给出了双特征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.

关 键 词：双特征Beltrami方程 P-调和方程 弱单调性 

分 类 号：O175.23[理学—数学] O174[理学—基础数学]