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
收藏
页数：19
相关论文
共 50 条
  • [1] Regularity of very weak solutions for elliptic equation of divergence form
    Zhang, Wei
    Bao, Jiguang
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (04) : 1867 - 1878
  • [2] PARTIAL REGULARITY FOR WEAK SOLUTIONS OF A NONLINEAR ELLIPTIC EQUATION
    PACARD, F
    [J]. MANUSCRIPTA MATHEMATICA, 1993, 79 (02) : 161 - 172
  • [3] Regularity for very weak solutions to A-harmonic equation
    Lin L.
    Gao H.
    [J]. Applied Mathematics-A Journal of Chinese Universities, 2006, 21 (3) : 343 - 349
  • [4] REGULARITY FOR VERY WEAK SOLUTIONS TO A-HARMONIC EQUATION
    Liu Lin Gao Hongya Applied Science School
    [J]. Applied Mathematics:A Journal of Chinese Universities, 2006, (03) : 343 - 349
  • [5] Regularity of very weak solutions for a class of nonlinear elliptic systems
    Zheng, SZ
    Fang, AN
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 1998, 14 : 733 - 740
  • [6] Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
    Qing Zhao
    Shuhong Chen
    [J]. Journal of Inequalities and Applications, 2017
  • [7] Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
    Zhao, Qing
    Chen, Shuhong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
  • [8] On the regularity of very weak solutions for linear elliptic equations in divergence form
    Domenico Angelo La Manna
    Chiara Leone
    Roberta Schiattarella
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2020, 27
  • [9] Regularity for Very Weak Solutions of A-Harmonic Equation with Weight
    Gao Hong-ya
    Zhang Yu
    Chu Yu-ming
    [J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2009, 49 (02): : 195 - 202
  • [10] On the regularity of very weak solutions for linear elliptic equations in divergence form
    La Manna, Domenico Angelo
    Leone, Chiara
    Schiattarella, Roberta
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2020, 27 (05):
12345