关于 Beltrami 方程组的很弱解

On Very Weak Solutions of Beltrami System

从考虑向量值函数的每一个分量出发，将Ｂｅｌｔｒａｍｉ方程组转化为一类散度型椭圆组；从而来建立Ｂｅｌｔｒａｍｉ方程组很弱解的正则性：存在可积指数ｒ１和ｒ２，１＜ｒ１＜ｎ＜ｒ２＜∞，使得方程组在低于自然可积指数Ｓｏｂｏｌｅｖ空间Ｗ１，ｒ１ｌｏｃ（Ω，Ｒｎ）中的很弱解，都属于空间Ｗ１，ｒ２ｌｏｃ（Ω，Ｒｎ）。

By considering each component of vector functions,we transform Beltrami system to a class of elliptic systems of divergence type.Then we establish the regularity of very weak solutions of Beltrami system:there exist integrable exponents r 1 and r 2 (1<r 1<n<r 2<∞) such that every very weak solution f∈W 1,r 1 loc (Ω,R n)of Beltrami system belongs to W 1,r 2 loc (Ω,R n).So f is still a classical weak solution of Beltrami system.