Elliptic equations with BMO nonlinearity in Reifenberg domains

被引：62

作者：

Byun, Sun-Sig ^{[1
]}

Wang, Lihe ^{[2
,3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[3] Xian Jiaotong Univ, Coll Sci, Xian 710049, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2008年 / 219卷 / 06期

基金：

美国国家科学基金会;

关键词：

Elliptic equations; BMO space; Maximal function; Regularity theory;

D O I：

10.1016/j.aim.2008.07.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given p epsilon [2, +infinity), we obtain the global W-1, p estimate for the weak solution of a boundary-value problem for an elliptic equation with BMO nonlinearity in a Reifenberg domain, assuming that the nonlinearity has sufficiently small BMO seminorm and that the boundary of the domain is sufficiently flat. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1937 / 1971

页数：35

共 29 条

[1] Gradient estimates for a class of parabolic systems [J].

Acerbi, Emilio ;

Mingione, Giuseppe .

DUKE MATHEMATICAL JOURNAL, 2007, 136 (02) :285-320

[2]

[Anonymous], HARMONIC ANAL

[3]

Auscher P, 2002, B UNIONE MAT ITAL, V5B, P487

[4] Elliptic equations with BMO coefficients in Reifenberg domains [J].

Byun, SS ;

Wang, LH .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (10) :1283-1310

[5] LP-estimates for general Nonlinear elliptic equations [J].

Byun, Sun-Sig ;

Wang, Lihe .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (06) :3193-3221

[6] Nonlinear elliptic equations with BMO coefficients in Reifenberg domains [J].

Byun, Sun-Sig ;

Wang, Lihe ;

Zhou, Shulin .

JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 250 (01) :167-196

[7] Parabolic equations in time dependent Reifenberg domains [J].

Byun, Sun-Sig ;

Wang, Lihe .

ADVANCES IN MATHEMATICS, 2007, 212 (02) :797-818

[8]

Caffarelli L. A., 1995, AM MATH SOC C PUBL, V43

[9] INTERIOR A PRIORI ESTIMATES FOR SOLUTIONS OF FULLY NON-LINEAR EQUATIONS [J].

CAFFARELLI, LA .

ANNALS OF MATHEMATICS, 1989, 130 (01) :189-213

[10]

Caffarelli LA, 1998, COMMUN PUR APPL MATH, V51, P1

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