一类拟线性椭圆型方程的很弱解的正则性

Regularity Result of Very Weak Solutions of aClass of Quasilinear Elliptic Equation

利用Hodge分解等工具研究了一类拟线性椭圆型方程:-div a(x,u,Du)=F(x,u),x∈Ω的很弱解,其中ΩRN为有界区域.通过能量估计,得到了上述很弱解的局部与全局正则性,并用Hodge分解取出了适当的试验函数,克服了证明中的困难,推广了有关文献的结果.

In this paper, we consider the regularity result of very weak solutions of a class of quasilinear elliptic equations：-div a（x,u,Du）=F（x,u）,x∈Ω is a bounded domain. By using the Hodge decomposition, we obtain the local and global regularity of very weak solutions for the above equation. We use some suitable test function to overcome some difficulty and extend the result of literature.