GLOBAL GRADIENT ESTIMATES FOR p(x)-LAPLACE EQUATION IN NON-SMOOTH DOMAINS

被引：3
|
作者：
Zhang, Chao [1 ]
Wang, Lihe [2 ,3 ]
Zhou, Shulin [4 ]
Kim, Yun-Ho [5 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
[3] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
[4] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China
[5] Sangmyung Univ, Dept Math Educ, Seoul 110743, South Korea
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 06期
基金：
中国博士后科学基金; 新加坡国家研究基金会; 高等学校博士学科点专项科研基金;
关键词：
Elliptic; p(x)-Laplacian; Gradient estimate; BMO space; Reifenberg domain; ELLIPTIC-EQUATIONS; VARIABLE EXPONENT; BMO COEFFICIENTS; REGULARITY; SPACES; INTEGRABILITY; FUNCTIONALS;
D O I：
10.3934/cpaa.2014.13.2559
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the global gradient estimates for weak solutions of p(x)-Laplacian type equation with small BMO coefficients in a delta-Reifenberg flat domain. The modified Vitali covering lemma, good lambda-inequalities, the maximal function technique and the appropriate localization method are the main analytical tools. The global Calderon-Zygmund theory for such equations is obtained. Moreover, we generalize the regularity estimates in the Lebesgue spaces to the Orlicz spaces.
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页码：2559 / 2587
页数：29
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