Quasiconvexification in W1,1 and optimal jump microstructure in BV relaxation

被引：12

作者：

Larsen, CJ ^{[1
]}

机构：

[1] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA

[2] Carnegie Mellon Univ, Pittsburgh, PA 15213 USA

[3] USA, Res Lab, Aberdeen, MD USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1998年 / 29卷 / 04期

关键词：

quasiconvex; lower semicontinuous; microstructure; bounded variation; relaxation;

D O I：

10.1137/S0036141095295991

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An integral representation for the relaxation in BV(Omega; R-p) of the functional u bar right arrow integral Omega W(del u(x))dx + HN-1 (S(u)) with respect to BV weak * convergence is obtained. The bulk term in the integral representation reduces to the quasiconvexification of W, and we describe optimal behavior of approximating sequences along S(u), for scalar valued u.

引用

页码：823 / 848

页数：26

共 17 条

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

ACERBI, E ;

FUSCO, N .

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

[2] RANK ONE PROPERTY FOR DERIVATIVES OF FUNCTIONS WITH BOUNDED VARIATION [J].

ALBERTI, G .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1993, 123 :239-274

[3]

AMBROSIO L, 1990, J MATH PURE APPL, V69, P285

[4]

AMBROSIO L, 1990, J MATH PURE APPL, V69, P307

[5] ON THE LOWER SEMICONTINUITY OF QUASI-CONVEX INTEGRALS IN SBV(OMEGA, R(K)) [J].

AMBROSIO, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (03) :405-425

[6]

[Anonymous], WEAKLY DIFFERENTIABL

[7] Relaxation of bulk and interfacial energies [J].

Barroso, AC ;

Bouchitte, G ;

Buttazzo, G ;

Fonseca, I .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1996, 135 (02) :107-173

[8]

BOUCHITTE G, 1995, J REINE ANGEW MATH, V458, P1

[9]

Dacorogna B., 1989, DIRECT METHODS CALCU

[10]

De Giorgi E., 1988, ATTI ACCAD NAZ SFMN, V82, P199

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