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Volumn 7, Issue , 2002, Pages 443-470

Equi-integrability results for 3D-2D dimension reduction problems

Author keywords

Concentrations; Dimension reduction; Equi integrability; Lower semicontinuity; Maximal function; Oscillations; Quasiconvexity

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; GRADIENT METHODS; INTEGRAL EQUATIONS; INTEGRATION; MATHEMATICAL MODELS; THEOREM PROVING; THREE DIMENSIONAL; TWO DIMENSIONAL;

EID: 0036412323     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2002063     Document Type: Article
Times cited : (20)

References (35)
  • 1
    • 34250138457 scopus 로고
    • Semicontinuity problems in the calculus of variations
    • E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational. Mech. Anal. 86 (1984) 125-145.
    • (1984) Arch. Rational. Mech. Anal. , vol.86 , pp. 125-145
    • Acerbi, E.1    Fusco, N.2
  • 3
    • 0028466769 scopus 로고
    • Dimensional reduction in variational problems, asymptotic developments in r-convergence, and thin structures in elasticity
    • E. Anzelotti, S. Baldo and D. Percivale, Dimensional reduction in variational problems, asymptotic developments in r-convergence, and thin structures in elasticity. Asymptot. Anal. 9 (1994) 61-100.
    • (1994) Asymptot. Anal. , vol.9 , pp. 61-100
    • Anzelotti, E.1    Baldo, S.2    Percivale, D.3
  • 4
    • 0021466176 scopus 로고
    • A general approach to lower semicontinuity and lower closure in optimal control theory
    • E.J. Balder, A general approach to lower semicontinuity and lower closure in optimal control theory. SIAM J. Control Optim. 22 (1984) 570-598.
    • (1984) SIAM J. Control Optim. , vol.22 , pp. 570-598
    • Balder, E.J.1
  • 5
    • 0000093666 scopus 로고
    • A version of the fundamental theorem for Young mesures
    • edited by M. Rascle, D. Serre and M. Slemrod. Springer-Verlag, Berlin, Lecture Notes in Phys
    • J.M. Ball, A version of the fundamental theorem for Young mesures, in PDE’s and Continuum Models of Phase Transitions, edited by M. Rascle, D. Serre and M. Slemrod. Springer-Verlag, Berlin, Lecture Notes in Phys. 344 (1989) 207-215.
    • (1989) PDE’s and Continuum Models of Phase Transitions , vol.344 , pp. 207-215
    • Ball, J.M.1
  • 6
    • 0000229008 scopus 로고
    • Integrands normales et mesures parametrees en calcul des variations
    • H. Berliocchi and J.-M. Lasry, Integrands normales et mesures parametrees en calcul des variations. Bull. Soc. Math. France 101 (1973) 129-184.
    • (1973) Bull. Soc. Math. France , vol.101 , pp. 129-184
    • Berliocchi, H.1    Lasry, J.-M.2
  • 9
    • 0033098284 scopus 로고    scopus 로고
    • A theory of thin films of martensitic materials with applications to microactuators
    • K. Bhattacharya and R.D. James, A theory of thin films of martensitic materials with applications to microactuators. J. Mech. Phys. Solids 47 (1999) 531-576.
    • (1999) J. Mech. Phys. Solids , vol.47 , pp. 531-576
    • Bhattacharya, K.1    James, R.D.2
  • 10
    • 84996139462 scopus 로고    scopus 로고
    • Private communication
    • A. Braides, Private communication.
    • Braides, A.1
  • 11
    • 0039030756 scopus 로고    scopus 로고
    • 3D-2D asymptotic analysis for inhomogeneous thin films
    • A. Braides, I. Fonseca and G. Francfort, 3D-2D asymptotic analysis for inhomogeneous thin films. Indiana Univ. Math. J. 49 (2000) 1367-1404.
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1367-1404
    • Braides, A.1    Fonseca, I.2    Francfort, G.3
  • 15
    • 0011188033 scopus 로고    scopus 로고
    • On the inadequacy of scaling of linear elasticity for 3D-2D asymptotics in a nonlinear setting
    • I. Fonseca and G. Francfort, On the inadequacy of scaling of linear elasticity for 3D-2D asymptotics in a nonlinear setting. J. Math. Pures Appl. 80 (2001) 547-562.
    • (2001) J. Math. Pures Appl. , vol.80 , pp. 547-562
    • Fonseca, I.1    Francfort, G.2
  • 17
    • 0040039871 scopus 로고    scopus 로고
    • Analysis of concentration and oscillation effects generated by gradients
    • I. Fonseca, S. Muller and P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 (1998) 736-756.
    • (1998) SIAM J. Math. Anal.. , vol.29 , pp. 736-756
    • Fonseca, I.1    Muller, S.2    Pedregal, P.3
  • 18
    • 21344486080 scopus 로고
    • A justification of nonlinear properly invariant plate theories
    • D.D. Fox, A. Raoult and J.C. Simo, A justification of nonlinear properly invariant plate theories. Arch. Rational. Mech. Anal. 124 (1993) 157-199.
    • (1993) Arch. Rational. Mech. Anal. , vol.124 , pp. 157-199
    • Fox, D.D.1    Raoult, A.2    Simo, J.C.3
  • 19
    • 21144464174 scopus 로고
    • On the integrability of the Jacobian under minimal hypotheses
    • T. Iwaniec and C. Sbordone, On the integrability of the Jacobian under minimal hypotheses. Arch. Rational. Mech. Anal. 119 (1992) 129-143.
    • (1992) Arch. Rational. Mech. Anal. , vol.119 , pp. 129-143
    • Iwaniec, T.1    Sbordone, C.2
  • 20
    • 0001139965 scopus 로고
    • Characterizations of Young mesures generated by gradients
    • D. Kinderlehrer and P. Pedregal, Characterizations of Young mesures generated by gradients. Arch. Rational. Mech. Anal. 115 (1991) 329-365.
    • (1991) Arch. Rational. Mech. Anal. , vol.115 , pp. 329-365
    • Kinderlehrer, D.1    Pedregal, P.2
  • 21
    • 0002444348 scopus 로고
    • Gradient Young mesures generated by sequences in Sobolev spaces
    • D. Kinderlehrer and P. Pedregal, Gradient Young mesures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59-90.
    • (1994) J. Geom. Anal. , vol.4 , pp. 59-90
    • Kinderlehrer, D.1    Pedregal, P.2
  • 23
    • 0033432488 scopus 로고    scopus 로고
    • Lower semicontinuity in spaces of weakly differentiable functions
    • J. Kristensen, Lower semicontinuity in spaces of weakly differentiable functions. Math. Ann. 313 (1999) 653-710.
    • (1999) Math. Ann. , vol.313 , pp. 653-710
    • Kristensen, J.1
  • 24
    • 0000312494 scopus 로고
    • The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
    • H. Le Dret and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl. 74 (1995) 549-578.
    • (1995) J. Math. Pures Appl. , vol.74 , pp. 549-578
    • Le Dret, H.1    Raoult, A.2
  • 25
    • 0034403659 scopus 로고    scopus 로고
    • Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results
    • H. Le Dret and A. Raoult, Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results. Arch. Rational. Mech. Anal. 154 (2000) 101-134.
    • (2000) Arch. Rational. Mech. Anal. , vol.154 , pp. 101-134
    • Le Dret, H.1    Raoult, A.2
  • 26
    • 0000708610 scopus 로고    scopus 로고
    • A Luzin type property of Sobolev functions
    • F.C. Liu, A Luzin type property of Sobolev functions. Indiana Univ. Math. J. 26 (1997) 645-651.
    • (1997) Indiana Univ. Math. J. , vol.26 , pp. 645-651
    • Liu, F.C.1
  • 29
    • 84965031674 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • edited by R. Knops. Longman, Harlow, Pitman Res. Notes Math. Ser
    • L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, edited by R. Knops. Longman, Harlow, Pitman Res. Notes Math. Ser. 39 (1979) 136-212.
    • (1979) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium , vol.39 , pp. 136-212
    • Tartar, L.1
  • 30
    • 0002851015 scopus 로고
    • The compensated compactness method applied to systems of conservation laws
    • edited by J.M. Ball. Riedel
    • L. Tartar, The compensated compactness method applied to systems of conservation laws, in Systems of Nonlinear Partial Differential Equations, edited by J.M. Ball. Riedel (1983).
    • (1983) Systems of Nonlinear Partial Differential Equations
    • Tartar, L.1
  • 31
    • 0001337359 scopus 로고
    • Étude des oscillations dans les équations aux dérivées partielles nonlinéaires
    • Springer-Verlag, Berlin
    • L. Tartar, Étude des oscillations dans les équations aux dérivées partielles nonlinéaires. Springer-Verlag, Berlin, Lecture Notes in Phys. 195 (1994) 384-412.
    • (1994) Lecture Notes in Phys , vol.195 , pp. 384-412
    • Tartar, L.1
  • 32
    • 0034422268 scopus 로고    scopus 로고
    • Heterogeneous thin films of martensitic materials
    • Y.C. Shu, Heterogeneous thin films of martensitic materials. Arch. Rational. Mech. Anal. 153 (2000) 39-90.
    • (2000) Arch. Rational. Mech. Anal. , vol.153 , pp. 39-90
    • Shu, Y.C.1
  • 33
    • 0001331327 scopus 로고
    • Generalized curves and the existence of an attained absolute minimum in the calculus of variations
    • L.C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations. C. R. Soc. Sci. Lettres de Varsovie, Classe III 30 (1937) 212-234.
    • (1937) C. R. Soc. Sci. Lettres De Varsovie, Classe III , vol.30 , pp. 212-234
    • Young, L.C.1


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