关于 Beltrami 方程组的很弱解  

On Very Weak Solutions of Beltrami System

作　　者：郑神州[1] 

机构地区：[1]北方交通大学文理学院

出　　处：《北方交通大学学报》1998年第2期12-18,共7页Journal of Northern Jiaotong University

摘　　要：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.

关 键 词：弱K拟正则映射 BELTRAMI方程组 很弱解 

分 类 号：O175.5[理学—数学]