Regularity results for minimizers of (2, q)-growth functionals in the Heisenberg Group

被引：1

作者：

Foeglein, Anna ^{[1
]}

机构：

[1] Univ Regensburg, NWF I Math, D-93040 Regensburg, Germany

来源：

MANUSCRIPTA MATHEMATICA | 2010年 / 133卷 / 1-2期

关键词：

QUASI-LINEAR EQUATIONS; ELLIPTIC-EQUATIONS; INTEGRAL FUNCTIONALS; INEQUALITY; CALCULUS; SPACES;

D O I：

10.1007/s00229-010-0366-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider integral functionals in the Heisenberg group, whose convex C-2-integrand has quadratic growth from below, and growth of order q > 2 from above. We prove Holder regularity for the full gradient of minimizers under the condition that q is less than an explicitly calculated dimension-dependent bound.

引用

页码：131 / 172

页数：42

共 46 条

[1]

Acerbi E, 2005, J REINE ANGEW MATH, V584, P117

[2] Regularity results for stationary electro-rheological fluids [J].

Acerbi, E ;

Mingione, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (03) :213-259

[3] Regularity results for a class of functionals with non-standard growth [J].

Acerbi, E ;

Mingione, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) :121-140

[4]

[Anonymous], 1991, Ric. Mat.

[5]

[Anonymous], 2006, Applications of mathematics, DOI DOI 10.1007/S10778-006-0110-3

[6]

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

[7]

2-3

[8] 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

[9]

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

[10] 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

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