EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 7 (2002) ESAIM: COCV, 7 (2002) 443-470 References
Free Access
Issue
ESAIM: COCV
Volume 7, 2002
Page(s) 443 - 470
DOI https://doi.org/10.1051/cocv:2002063
Published online 15 September 2002
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational. Mech. Anal. 86 (1984) 125-145. [Google Scholar]
  2. E. Acerbi and N. Fusco, An approximation lemma for W1,pfunctions, in Material Instabilities in Continuum Mechanics and Related Mathematical Problems, edited by J.M. Ball. Heriot-Watt University, Oxford (1988). [Google Scholar]
  3. E. Anzelotti, S. Baldo and D. Percivale, Dimensional reduction in variational problems, asymptotic developments in Formula -convergence, and thin structures in elasticity. Asymptot. Anal. 9 (1994) 61-100. [Google Scholar]
  4. E.J. Balder, A general approach to lower semicontinuity and lower closure in optimal control theory. SIAM J. Control Optim. 22 (1984) 570-598. [CrossRef] [MathSciNet] [Google Scholar]
  5. 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. [Google Scholar]
  6. H. Berliocchi and J.-M. Lasry, Intégrands normales et mesures paramétrées en calcul des variations. Bull. Soc. Math. France 101 (1973) 129-184. [MathSciNet] [Google Scholar]
  7. K. Bhattacharya and A. Braides, Thin films with many small cracks. Preprint (2000). [Google Scholar]
  8. K. Bhattacharya, I. Fonseca and G. Francfort, An asymptotic study of the debonding of thin films. Arch. Rational. Mech. Anal. 161 (2002) 205-229. [CrossRef] [Google Scholar]
  9. 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. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Braides, Private communication. [Google Scholar]
  11. A. Braides, I. Fonseca and G. Francfort, 3D-2D asymptotic analysis for inhomogeneous thin films. Indiana Univ. Math. J. 49 (2000) 1367-1404. [MathSciNet] [Google Scholar]
  12. A. Braides and I. Fonseca, Brittle thin films. Appl. Math. Optim. 44 (2001) 299-323. [CrossRef] [MathSciNet] [Google Scholar]
  13. S. Conti, I. Fonseca and G. Leoni, A Formula -convergence result for the two-gradient theory of phase transitions, Preprint 01-CNA-008. Center for Nonlinear Analysis, Carnegie Mellon University (2001). Comm. Pure Applied Math. (to appear). [Google Scholar]
  14. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer-Verlag (1989). [Google Scholar]
  15. 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. [CrossRef] [MathSciNet] [Google Scholar]
  16. I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations with Applications to Nonlinear Continuum Physics. Springer-Verlag (to appear). [Google Scholar]
  17. I. Fonseca, S. Müller and P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 (1998) 736-756. [CrossRef] [MathSciNet] [Google Scholar]
  18. 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. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. Iwaniec and C. Sbordone, On the integrability of the Jacobian under minimal hypotheses. Arch. Rational. Mech. Anal. 119 (1992) 129-143. [CrossRef] [MathSciNet] [Google Scholar]
  20. D. Kinderlehrer and P. Pedregal, Characterizations of Young mesures generated by gradients. Arch. Rational. Mech. Anal. 115 (1991) 329-365. [Google Scholar]
  21. D. Kinderlehrer and P. Pedregal, Gradient Young mesures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59-90. [Google Scholar]
  22. J. Kristensen, Finite functionals and Young measures generated by gradients of Sobolev functions. Mathematical Institute, Technical University of Denmark, Mat-Report No. 1994-34 (1994). [Google Scholar]
  23. J. Kristensen, Lower semicontinuity in spaces of weakly differentiable functions. Math. Ann. 313 (1999) 653-710. [CrossRef] [MathSciNet] [Google Scholar]
  24. 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. [MathSciNet] [Google Scholar]
  25. 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. [Google Scholar]
  26. F.C. Liu, A Luzin type property of Sobolev functions. Indiana Univ. Math. J. 26 (1997) 645-651. [Google Scholar]
  27. P. Pedregal, Parametrized mesures and Variational Principles. Birkhäuser, Boston (1997). [Google Scholar]
  28. E.M. Stein, Singular integrals and differentiability properties of functions. Princeton University Press (1970). [Google Scholar]
  29. 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. [Google Scholar]
  30. 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). [Google Scholar]
  31. L. Tartar, Étude des oscillations dans les équations aux dérivées partielles nonlinéaires. Springer-Verlag, Berlin, Lecture Notes in Phys. 195 (1994) 384-412. [Google Scholar]
  32. Y.C. Shu, Heterogeneous thin films of martensitic materials. Arch. Rational. Mech. Anal. 153 (2000) 39-90. [CrossRef] [Google Scholar]
  33. 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. [Google Scholar]
  34. L.C. Young, Lectures on the calculus of variations and optimal control theory. W.B. Saunders (1969). [Google Scholar]
  35. W.P. Ziemer, Weakly Differentiable Functions. Sobolev spaces and functions of bounded variation. Springer-Verlag, Berlin (1989). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.