Regularity of very weak solutions for elliptic equation of divergence form

被引：8

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：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262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; BOUNDARY SINGULARITIES; DISTANCE; RESPECT;

D O I：

10.1016/j.jfa.2011.11.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the local regularity of very weak solution mu is an element of L-loc(1)(ohm) of the elliptic equation D-j(a(ij)(x)D(i)u) = 0. Using the bootstrap argument and the difference quotient method, we obtain that if a(ij) is an element of C-loc(0,1)(ohm), then u is an element of W-loc(2,p)(ohm) for any p < infinity. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1867 / 1878

页数：12

共 20 条

[1] Elliptic operators, conormal derivatives and positive parts of functions (with an appendix by Haim Brezis) [J].