关于广义Beltrami方程组

数学物理学报 ›› 2010, Vol. 30 ›› Issue (4): 953-958.

关于广义Beltrami方程组

高红亚^1,2, 赵丽芳¹

1.河北大学数学与计算机学院河北保定 071002|2.河北省数学研究中心石家庄 050016

收稿日期:2008-08-10 修回日期:2009-06-02 出版日期:2010-07-25 发布日期:2010-07-25
基金资助:
国家自然科学基金(10971224)和河北省自然科学基金数学研究专项(07M003)资助

On Generalized Beltrami System

GAO Hong-Ya^1,2, ZHAO Li-Fang¹

1.College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002;
2.Mathematical Study Center of Hebei Province, Shijiazhuang 050016

Received:2008-08-10 Revised:2009-06-02 Online:2010-07-25 Published:2010-07-25
Supported by:
国家自然科学基金(10971224)和河北省自然科学基金数学研究专项(07M003)资助

摘要/Abstract

摘要：

该文考虑广义Beltrami方程组
D^tf(x)H(x)Df(x)=J(x, f)^2/nG(x). (*)
利用能量和变分方法, 在矩阵H(x), G(x) ∈S(n)满足一致椭圆型条件下, 得到了(*)式所满足的齐次散度型椭圆方程
Div A(x, Df(x))=0
并得到了(*)式的分量函数的弱单调性和Caccioppoli不等式.

关键词: Beltrami方程组;散度型椭圆方程, 能量泛函, 弱单调性, Caccioppoli不等式

Abstract:

This paper deals with the generalized Beltrami system
D^tf(x)H(x)Df(x)=J(x, f)^2/nG(x). (*)
A homogeneous elliptic equation of divergence type
Div A(x, Df(x))=0
is derived from (*) under the uniformly elliptic conditions on the matrices H(x), G(x) ∈S(n) by using the energy and variational methods. The weak monotonicity properties for the component functions of (*) and a Caccioppoli inequality are also derived.

Key words: Beltrami system, Elliptic equation of divergence type, Energy functional, Weak monotonicity, Caccioppoli inequality

中图分类号:

30C65

高红亚, 赵丽芳. 关于广义Beltrami方程组[J]. 数学物理学报, 2010, 30(4): 953-958.

GAO Hong-Ya, ZHAO Li-Fang. On Generalized Beltrami System[J]. Acta mathematica scientia,Series A, 2010, 30(4): 953-958.

[1]	高红亚, 王红敏, 顾广泽. Beltrami方程组弱解分量函数的弱单调性[J]. 数学物理学报, 2009, 29(3): 651-655.
[2]	高红亚, 吴泽民. 关于双特征Beltrami方程[J]. 数学物理学报, 2002, 22(4): 433-440.