一类椭圆方程很弱解的正则性

Regularity for the Very Weak Solutions of a Class of Elliptic Equation

得到了一类二阶椭圆方程Lu=f很弱解的一个临界情形的正则性结果.它指出:若|f|log+|f|∈L1(Ω),则u∈L n/n-2(Ω).另外若对区域以及系数附加一定的正则性条件,并设|f|log+|f|∈L1(Ω),则:|(?)u|∈Ln/n-1(Ω).

In this paper, we considered the second order elliptic equation: Lu = f, and got a regularity result in limit cases for the very weak solutions of the equation, we show: let |f|log+ |f| , then ; with addition assumption on the domain and coefficients, and futhermore , then .