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Volumn 134, Issue 5, 2004, Pages 845-883

A Young measure approach to a nonlinear membrane model involving the bending moment

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EID: 10044287116     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500003516     Document Type: Conference Paper
Times cited : (7)

References (31)
  • 1
    • 34250138457 scopus 로고
    • Semicontinuity problems in the calculus of variations
    • E. Acerbi and N. Fusco. Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Analysis 86 (1984), 125-145.
    • (1984) Arch. Ration. Mech. Analysis , vol.86 , pp. 125-145
    • Acerbi, E.1    Fusco, N.2
  • 2
    • 0028466769 scopus 로고
    • Dimensional reduction in variational problems, asymptotic developments in Γ-convergence and thin structures in elasticity
    • E. Anzelotti, S. Baldo and D. Percivale. Dimensional reduction in variational problems, asymptotic developments in Γ-convergence and thin structures in elasticity. Asymp. Analysis 9 (1994), 61-100.
    • (1994) Asymp. Analysis , 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 measures
    • (ed. M. Rascle, D. Serre and M. Slemrod). Lecture Notes in Physics, Springer
    • J. M. Ball. A version of the fundamental theorem for Young measures. In PDEs and continuum models of phase transitions (ed. M. Rascle, D. Serre and M. Slemrod). Lecture Notes in Physics, vol. 344, pp. 207-215 (Springer, 1989).
    • (1989) PDEs and Continuum Models of Phase Transitions , vol.344 , pp. 207-215
    • Ball, J.M.1
  • 6
    • 0000229008 scopus 로고
    • Intégrands normales et mesures paramétrées en calcul des variations
    • H. Berliocchi and J.-M. Lasry. Intégrands normales et mesures paramétrées en calcul des variations. Bull. Soc. Math. Prance 101 (1973), 129-184.
    • (1973) Bull. Soc. Math. Prance , vol.101 , pp. 129-184
    • Berliocchi, H.1    Lasry, J.-M.2
  • 7
    • 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
  • 9
    • 10044242938 scopus 로고    scopus 로고
    • Young measure minimizers in the asymptotic analysis of thin films
    • Center for Nonlinear Analysis, Carnegie Mellon University
    • M. Bocea. Young measure minimizers in the asymptotic analysis of thin films. Scientific Report 03-CNA-002, Center for Nonlinear Analysis, Carnegie Mellon University (2003).
    • (2003) Scientific Report 03-CNA-002
    • Bocea, M.1
  • 10
    • 0036412323 scopus 로고    scopus 로고
    • Equi-integrability results for 3D-2D dimension reduction problems
    • M. Bocea and I. Fonseca. Equi-integrability results for 3D-2D dimension reduction problems. ESAIM: Control Optim. Calc. Variations 7 (2002), 443-470.
    • (2002) ESAIM: Control Optim. Calc. Variations , vol.7 , pp. 443-470
    • Bocea, M.1    Fonseca, I.2
  • 11
    • 10044266917 scopus 로고    scopus 로고
    • Bending moment in membrane theory
    • Center for Nonlinear Analysis, Carnegie Mellon University
    • G. Bouchitté, I. Fonseca and M. L. Mascarenhas. Bending moment in membrane theory. Scientific Report 02-CNA-016, Center for Nonlinear Analysis, Carnegie Mellon University (2002).
    • (2002) Scientific Report 02-CNA-016
    • Bouchitté, G.1    Fonseca, I.2    Mascarenhas, M.L.3
  • 13
    • 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
  • 16
    • 0033249123 scopus 로고    scopus 로고
    • A-quasiconvexity, lower semicontinuity, and Young measures
    • I. Fonseca and S. Müller. A-quasiconvexity, lower semicontinuity, and Young measures. SIAM J. Math. Analysis 30 (1999), 1355-1390.
    • (1999) SIAM J. Math. Analysis , vol.30 , pp. 1355-1390
    • Fonseca, I.1    Müller, S.2
  • 17
    • 0040039871 scopus 로고    scopus 로고
    • Analysis of concentration and oscillation effects generated by gradients
    • I. Fonseca, S. Müller and P. Pedregal. Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Analysis 29 (1998), 736-756.
    • (1998) SIAM J. Math. Analysis , vol.29 , pp. 736-756
    • Fonseca, I.1    Müller, S.2    Pedregal, P.3
  • 19
    • 0001139965 scopus 로고
    • Characterizations of young measures generated by gradients
    • D. Kinderlehrer and P. Pedregal. Characterizations of Young measures generated by gradients. Arch. Ration. Mech. Analysis 115 (1991), 329-365.
    • (1991) Arch. Ration. Mech. Analysis , vol.115 , pp. 329-365
    • Kinderlehrer, D.1    Pedregal, P.2
  • 20
    • 0002444348 scopus 로고
    • Gradient young measures generated by sequences in sobolev spaces
    • D. Kinderlehrer and P. Pedregal. Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Analysis 4 (1994), 59-90.
    • (1994) J. Geom. Analysis , vol.4 , pp. 59-90
    • Kinderlehrer, D.1    Pedregal, P.2
  • 21
    • 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
  • 22
    • 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
  • 23
    • 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. Ration. Mech. Analysis 154 (2000), 101-134.
    • (2000) Arch. Ration. Mech. Analysis , vol.154 , pp. 101-134
    • Le Dret, H.1    Raoult, A.2
  • 24
    • 84972497511 scopus 로고
    • Quasiconvexity and the semicontinuity of multiple integrals
    • C. B. Morrey. Quasiconvexity and the semicontinuity of multiple integrals. Pac. J. Math. 2 (1952), 25-53.
    • (1952) Pac. J. Math. , vol.2 , pp. 25-53
    • Morrey, C.B.1
  • 27
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • (ed. R. Knops), vol. IV. Pitman Research Notes in Mathematics, New York: Longman
    • L. Tartar. Compensated compactness and applications to partial differential equations. In Nonlinear analysis and mechanics: Heriot-Watt symposium (ed. R. Knops), vol. IV. Pitman Research Notes in Mathematics, vol. 39, pp. 136-212 (New York: Longman, 1979).
    • (1979) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium , vol.39 , pp. 136-212
    • Tartar, L.1
  • 28
    • 0002851015 scopus 로고
    • The compensated compactness method applied to systems of conservation laws
    • (ed. J. M. Ball) Dordrecht: Reidel
    • L. Tartar. The compensated compactness method applied to systems of conservation laws. In Systems of nonlinear partial differential equations (ed. J. M. Ball) (Dordrecht: Reidel, 1983).
    • (1983) Systems of Nonlinear Partial Differential Equations
    • Tartar, L.1
  • 29
    • 0021649734 scopus 로고
    • Étude des oscillations dans les équations aux dérivées partielles nonlinéaires
    • Lecture Notes in Physics, Springer
    • L. Tartar. Étude des oscillations dans les équations aux dérivées partielles nonlinéaires. In Trends and applications of pure mathematics to mechanics. Lecture Notes in Physics, vol. 195, pp. 384-412 (Springer, 1984).
    • (1984) Trends and Applications of Pure Mathematics to Mechanics , vol.195 , pp. 384-412
    • Tartar, L.1
  • 30
    • 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. Lett. Varsovie Classe III 30 (1937), 212-234.
    • (1937) C. R. Soc. Sci. Lett. Varsovie Classe III , vol.30 , pp. 212-234
    • Young, L.C.1


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