Beltrami System With Two Characteristic Matrices In High Dimensional Spaces

In this paper, we consider Beltrami system with two characteristics in high-dimensional domains, where H(x)= diagi is diagonal with det H(x)= 1, and G(x)∈S(n) is a positive definite, symmetric matrix with deter-minant 1. A divergence type equation DivA(x,Df)= 0 is derived under some elliptic conditions on the matrices H(x) and G(x). The monotonicity, controlled growth, and homogeneous conditions for the operator A are obtained. As a consequence, Caccioppoli type inequality for the generalized solutions of the former equation is obtained.