双特征Beltrami方程组广义解的Caccioppoli不等式

Caccioppoli Inequality for GenerAlized Solutions of Beltrami System with Two Characteristic Matrices

考虑高维区域中的具有两个特征矩阵的Beltrami方程组D^tf(x)H(x)Df(x)=J(x,f)^(2/n)G(x)(*)在矩阵H(x),G(x)∈S(n)的一致椭圆型条件下,利用能量泛函和变分方法,得到了方程组(*)广义解的Caccioppoli不等式.

We consider the Beltrami system with two characteristic matrices D^tf（x）H（x）Df（x）=J（x,f）^2/nG（x）（＊） in high-dimensional domains. Under uniformly elliptic conditions on the matrices H（x）, G（x） ∈ S（n）, the Caccioppoli inequality for the generalized solutions of the equation （＊） is derived by using energy functional and variational methods.