Beltrami System With Two Characteristic Matrices In High-dimensional Spaces

Beltrami system with two characteristic matrices in high dimensional domains is a generalization of the Beltrami system with one characteristic matrix, which has al-ready been extensively researched. In this paper, we study Beltrami system with two characteristic matrices Dtf(x)H(x)Df(x)= J(x,f)2/nG(x). in high dimensional spaces. We obtain the corresponding homogeneous divergence-type equation DivA(x)Df(x))=0 for the Beltrami system with two characteristic matrices by using the energy and vari-ational methods under the uniformly elliptic conditions on H(x),G(x)∈GL(n). The Lipschitz-type, monotone and n - 1 homogeneous conditions are also obtained. The weak monotonicity result for the component functions of the Beltrami system with two characteristic matrices is obtained by using the homogeneous divergence-type equation.