Optimal partial regularity of second order parabolic systems under controllable growth condition

被引：8

作者：

Chen, Shuhong ^{[1
]}

Tan, Zhong ^{[2
]}

机构：

[1] Minnan Normal Univ, Sch Math & Stat, Zhangzhou 363000, Fujian, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Nonlinear parabolic systems; Controllable growth condition; A-caloric approximation; Optimal partial regularity; INTERIOR PARTIAL REGULARITY; NONLINEAR ELLIPTIC-SYSTEMS; HARMONIC APPROXIMATION; MINIMIZERS;

D O I：

10.1016/j.jfa.2014.02.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the regularity for weak solutions of second order nonlinear parabolic systems under controllable growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione. (C) 2014 Published by Elsevier Inc.

引用

页码：4908 / 4937

页数：30

共 20 条

[1]

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

[2] ON THE NONLINEAR PARABOLIC-SYSTEMS IN DIVERGENCE FORM - HOLDER CONTINUITY AND PARTIAL HOLDER CONTINUITY OF THE SOLUTIONS [J].

CAMPANATO, S .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1984, 137 :83-122

[3]

Campanato S., 1966, ANN MAT PUR APPL, V73, P55, DOI [10.1007/BF02415082, DOI 10.1007/BF02415082]

[4] The method of p-harmonic approximation and optimal interior partial regularity for energy minimizing p-harmonic maps under the controllable growth condition [J].

Chen, Shu-hong ;

Tan, Zhong .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2007, 50 (01) :105-115

[5] 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

[6] Optimal Interior Partial Regularity for Nonlinear Elliptic Systems for the Case 1 < m < 2 under Natural Growth Condition [J].

Chen, Shuhong ;

Tan, Zhong .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,

[7] OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS [J].

Chen, Shuhong ;

Tan, Zhong .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (03) :981-993

[8]

Da Prato G., 1965, Ann. Mat. Pura Appl., V69, P383, DOI 10.1007/BF02414378

[9]

De Giorgi E., 1960, SEM MAT SCUOLA NORMA

[10] Second order parabolic systems, optimal regularity, and singular sets of solutions [J].

Duzaar, F ;

Mingione, G .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2005, 22 (06) :705-751

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