Optimal partial regularity for weak solutions of nonlinear sub-elliptic systems in Carnot groups

被引：25

作者：

Wang, Jialin ^{[1
,2
]}

Niu, Pengcheng ^{[2
]}

机构：

[1] Gannan Normal Univ, Key Lab Numer Simulat Technol Jiangxi Prov, Ganzhou 341000, Jiangxi, Peoples R China

[2] NW Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 11期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

Carnot group; Nonlinear sub-elliptic system; Super-quadratic structure condition; Optimal partial regularity; A-harmonic approximation technique; INTERIOR PARTIAL REGULARITY; A-HARMONIC APPROXIMATION; QUASI-LINEAR EQUATIONS; HEISENBERG-GROUP; SUBELLIPTIC EQUATIONS; GROWTH CONDITION; HORMANDER TYPE; VECTOR-FIELDS; P-LAPLACIAN; OPERATORS;

D O I：

10.1016/j.na.2010.01.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with partial regularity for weak solutions to nonlinear sub-elliptic systems in divergence form in Carnot groups. The technique of A-harmonic approximation introduced by Simon and developed by Duzaar and Grotowski is adapted to our context. We establish Caccioppoli type inequalities and partial regularity with optimal local Holder exponents for horizontal gradients of weak solutions to systems under super-quadratic natural structure conditions and super-quadratic controllable structure conditions, respectively. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：4162 / 4187

页数：26

共 34 条

[1]

[Anonymous], 1968, Boll. Unione Mat. Ital.

[2]

[Anonymous], 1983, LECT GEOMETRIC MEASU

[3] Lp estimates for nonvariational hypoelliptic operators with VMO coefficients [J].

Bramanti, M ;

Brandolini, L .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (02) :781-822

[4] Schauder estimates for parabolic nondivergence operators of Hormander type [J].

Bramanti, Marco ;

Brandolini, Luca .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 234 (01) :177-245

[5]

Capogna L, 1997, COMMUN PUR APPL MATH, V50, P867, DOI 10.1002/(SICI)1097-0312(199709)50:9<867::AID-CPA3>3.0.CO

[6]

2-3

[7] Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hormander type [J].

Capogna, L ;

Garofalo, N .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2003, 5 (01) :1-40

[8]

Capogna L, 1999, MATH ANN, V313, P263, DOI 10.1007/s002080050261

[9] AN EMBEDDING THEOREM AND THE HARNACK INEQUALITY FOR NONLINEAR SUBELLIPTIC EQUATIONS [J].

CAPOGNA, L ;

DANIELLI, D ;

GAROFALO, N .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (9-10) :1765-1794

[10] The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition [J].

Chen, Shuhong ;

Tan, Zhong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (01) :20-42

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