Partial regularity for polyconvex functionals depending on the Hessian determinant

被引：2

作者：

Carozza, Menita ^{[1
]}

Leone, Chiara ^{[2
]}

di Napoli, Antonia Passarelli ^{[2
]}

Verde, Anna ^{[2
]}

机构：

[1] Univ Sannio, Dipartimento Pe Me Is, I-82100 Benevento, Italy

[2] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 35卷 / 02期

关键词：

QUASI-CONVEX INTEGRALS; VARIATIONAL INTEGRALS; MINIMIZERS; SEMICONTINUITY; THEOREM; ENERGY;

D O I：

10.1007/s00526-008-0203-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a C-2,C-alpha partial regularity result for local minimizers of polyconvex variational integrals of the type I(u) = integral(Omega)vertical bar D(2)u vertical bar(2) + g(det(D(2)u))dx, where Omega is a bounded open subset of R-2, u is an element of W-loc(2,2)(Omega) and g is an element of C-2(R) is a convex function, with subquadratic growth.

引用

页码：215 / 238

页数：24

共 33 条

[1]

ACERBI E, 1987, ARCH RATION MECH AN, V99, P261

[2] REGULARITY FOR MINIMIZERS OF NON-QUADRATIC FUNCTIONALS - THE CASE 1-LESS-THAN-P-LESS-THAN-2 [J].

ACERBI, E ;

FUSCO, N .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 140 (01) :115-135

[3] SEMICONTINUITY PROBLEMS IN THE CALCULUS OF VARIATIONS [J].

ACERBI, E ;

FUSCO, N .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1984, 86 (02) :125-145

[4]

BALL JM, 1977, ARCH RATION MECH AN, V63, P337, DOI 10.1007/BF00279992

[5]

Bildhauer M, 2001, ANN ACAD SCI FENN-M, V26, P509

[6] A regularity theorem for minimisers of quasiconvex integrals: The case 1<p<2 [J].

Carozza, M ;

diNapoli, AP .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 :1181-1199

[7] Partial regularity of local minimizers of quasiconvex integrals with sub-quadratic growth [J].

Carozza, M ;

di Napoli, AP .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 :1249-1262

[8] Partial Regularity of Minimizers of Quasiconvex Integrals with Subquadratic Growth [J].

Carozza, Menita ;

Fusco, Nicola ;

Mingione, Giuseppe .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1998, 175 (01) :141-164

[9] Partial regularity for anisotropic functionals of higher order [J].

Carozza, Menita ;

di Napoli, Antonia Passarelli .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2007, 13 (04) :692-706

[10]

Carriero M., 1997, ANN SC NORM SUPER PI, V25, P257

← 1 2 3 4 →