摘要
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ΩRN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.
出处
《河南大学学报(自然科学版)》
CAS
北大核心
2014年第4期379-383,共5页
Journal of Henan University:Natural Science
基金
国家自然科学基金资助(11201119)
关键词
拟线性椭圆型方程
很弱解
正则性
HODGE分解
quasilinear elliptic equation
very weak solution
regularity
Hodge decomposition