REGULARITY OF VERY WEAK SOLUTIONS FOR NONHOMOGENEOUS ELLIPTIC EQUATION

被引：10

作者：

Zhang, Wei ^{[1
]}

Bao, Jiguang ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2013年 / 15卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Very weak solution; regularity; linear elliptic equation; Sobolev space; Orlicz space; BOUNDARY SINGULARITIES; DISTANCE; RESPECT;

D O I：

10.1142/S0219199713500120

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the local regularity of very weak solution u is an element of L-loc(1) (Omega) of the elliptic equation D-j(a(ij)(x)D(i)u) = f - D(i)g(i). Using the bootstrap argument and the difference quotient method, we obtain that if a(ij) is an element of C-loc(0,1) (Omega), g(i) is an element of L-loc(p) (Omega) and f is an element of L-loc(Op) (Omega) with 1 < p < infinity, then u is an element of W-loc(1,p) (Omega). Furthermore, we consider the higher regularity of u.

引用

页数：19

共 23 条

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Adamas R. A., 2003, SOBOLEV SPACES

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