Free Access
Volume 16, Number 2, April-June 2010
Page(s) 472 - 502
Published online 21 April 2009
  1. J.J. Alibert and G. Bouchitté, Non-uniform integrability and generalized Young measures. J. Convex Anal. 4 (1997) 125–145. [Google Scholar]
  2. J.M. Ball, A version of the fundamental theorem for Young measures, in PDEs and Continuum Models of Phase Transition, M. Rascle, D. Serre and M. Slemrod Eds., Lect. Notes Phys. 344, Springer, Berlin (1989) 207–215. [Google Scholar]
  3. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  4. J.M. Ball and K.-W. Zhang, Lower semicontinuity of multiple integrals and the biting lemma. Proc. Roy. Soc. Edinb. A 114 (1990) 367–379. [Google Scholar]
  5. A. Braides, I. Fonseca and G. Leoni, A-quasiconvexity: relaxation and homogenization. ESAIM: COCV 5 (2000) 539–577. [CrossRef] [EDP Sciences] [Google Scholar]
  6. J.K. Brooks and R.V. Chacon, Continuity and compactness in measure. Adv. Math. 37 (1980) 16–26. [CrossRef] [Google Scholar]
  7. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer, Berlin (1989). [Google Scholar]
  8. A. DeSimone, Energy minimizers for large ferromagnetic bodies. Arch. Rat. Mech. Anal. 125 (1993) 99–143. [CrossRef] [Google Scholar]
  9. R.J. DiPerna and A.J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations. Commun. Math. Phys. 108 (1987) 667–689. [Google Scholar]
  10. N. Dunford and J.T. Schwartz, Linear Operators, Part I. Interscience, New York (1967). [Google Scholar]
  11. R. Engelking, General topology. Second Edition, PWN, Warszawa (1985). [Google Scholar]
  12. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Inc. Boca Raton (1992). [Google Scholar]
  13. I. Fonseca, Lower semicontinuity of surface energies. Proc. Roy. Soc. Edinb. A 120 (1992) 95–115. [Google Scholar]
  14. I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces. Springer (2007). [Google Scholar]
  15. I. Fonseca and S. Müller, Formula -quasiconvexity, lower semicontinuity, and Young measures. SIAM J. Math. Anal. 30 (1999) 1355–1390. [CrossRef] [MathSciNet] [Google Scholar]
  16. 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]
  17. J. Hogan, C. Li, A. McIntosh and K. Zhang, Global higher integrability of Jacobians on bounded domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 193–217. [Google Scholar]
  18. A. Kałamajska and M. Kružík, Oscillations and concentrations in sequences of gradients. ESAIM: COCV 14 (2008) 71–104. [CrossRef] [EDP Sciences] [Google Scholar]
  19. D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rat. Mech. Anal. 115 (1991) 329–365. [Google Scholar]
  20. D. Kinderlehrer and P. Pedregal, Weak convergence of integrands and the Young measure representation. SIAM J. Math. Anal. 23 (1992) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  21. D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59–90. [Google Scholar]
  22. J. Kristensen, Lower semicontinuity in spaces of weakly differentiable functions. Math. Ann. 313 (1999) 653–710. [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Kružík and T. Roubíček, Explicit characterization of Lp-Young measures. J. Math. Anal. Appl. 198 (1996) 830–843. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Kružík and T. Roubíček, On the measures of DiPerna and Majda. Mathematica Bohemica 122 (1997) 383–399. [MathSciNet] [Google Scholar]
  25. M. Kružík and T. Roubíček, Optimization problems with concentration and oscillation effects: relaxation theory and numerical approximation. Numer. Funct. Anal. Optim. 20 (1999) 511–530. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Licht, G. Michaille and S. Pagano, A model of elastic adhesive bonded joints through oscillation-concentration measures. J. Math. Pures Appl. 87 (2007) 343–365. [CrossRef] [MathSciNet] [Google Scholar]
  27. P. Marcellini, Approximation of quasiconvex functions and lower semicontinuity of multiple integrals. Manuscripta Math. 51 (1985) 1–28. [Google Scholar]
  28. C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer, Berlin (1966). [Google Scholar]
  29. S. Müller, Higher integrability of determinants and weak convergence in L1. J. Reine Angew. Math. 412 (1990) 20–34. [MathSciNet] [Google Scholar]
  30. S. Müller, Variational models for microstructure and phase transisions. Lect. Notes Math. 1713 (1999) 85–210. [CrossRef] [Google Scholar]
  31. P. Pedregal, Relaxation in ferromagnetism: the rigid case, J. Nonlinear Sci. 4 (1994) 105–125. [Google Scholar]
  32. P. Pedregal, Parametrized Measures and Variational Principles. Birkäuser, Basel (1997). [Google Scholar]
  33. T. Roubíček, Relaxation in Optimization Theory and Variational Calculus. W. de Gruyter, Berlin (1997). [Google Scholar]
  34. M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations. Comm. Partial Diff. Eq. 7 (1982) 959–1000. [Google Scholar]
  35. L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics, R.J. Knops Ed., Heriott-Watt Symposium IV, Pitman Res. Notes in Math. 39, San Francisco (1979). [Google Scholar]
  36. L. Tartar, Mathematical tools for studying oscillations and concentrations: From Young measures to H-measures and their variants, in Multiscale problems in science and technology. Challenges to mathematical analysis and perspectives, N. Antonič, C.J. Van Duijin and W. Jager Eds., Proceedings of the conference on multiscale problems in science and technology, held in Dubrovnik, Croatia, September 3–9, 2000, Springer, Berlin (2002). [Google Scholar]
  37. M. Valadier, Young measures, in Methods of Nonconvex Analysis, A. Cellina Ed., Lect. Notes Math. 1446, Springer, Berlin (1990) 152–188. [Google Scholar]
  38. J. Warga, Optimal Control of Differential and Functional Equations. Academic Press, New York (1972). [Google Scholar]
  39. L.C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations. Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, Classe III 30 (1937) 212–234. [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.