Free Access
Volume 19, Number 3, July-September 2013
Page(s) 679 - 700
Published online 17 May 2013
  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. Lect. Notes Phys., vol. 344, edited by M. Rascle, D. Serre and M. Slemrod. Springer, Berlin (1989) 207–215. [Google Scholar]
  3. J.M. Ball and J. Marsden, Quasiconvexity at the boundary, positivity of the second variation and elastic stability. Arch. Ration. Mech. Anal. 86 (1984) 251–277. [Google Scholar]
  4. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  5. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer, Berlin (1989). [Google Scholar]
  6. R.J. Di Perna and A.J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations. Comm. Math. Phys. 108 (1987) 667–689. [CrossRef] [MathSciNet] [Google Scholar]
  7. N. Dunford and J.T. Schwartz, Linear Operators, Part I, Interscience, New York (1967). [Google Scholar]
  8. R. Engelking, General topology, 2nd edition. PWN, Warszawa (1985). [Google Scholar]
  9. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Inc. Boca Raton (1992). [Google Scholar]
  10. I. Fonseca, Lower semicontinuity of surface energies. Proc. Roy. Soc. Edinburgh 120A (1992) 95–115. [Google Scholar]
  11. I. Fonseca and M. Kruížk, Oscillations and concentrations generated by 𝒜-free mappings and weak lower semicontinuity of integral functionals. ESAIM: COCV 16 (2010) 472–502. [CrossRef] [EDP Sciences] [Google Scholar]
  12. 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]
  13. Y. Grabovskya and T. Mengesha, Direct approach to the problem of strong local minima in calculus of variations. Calc. Var. 29 (2007) 59–83. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Hogan, C. Li, A. McIntosh and K. Zhang, Global higher integrability of Jacobians on bounded domains. Ann. l’Inst. Henri Poincaré Sect. C 17 (2000) 193–217. [Google Scholar]
  15. A. Kałamajska and M. Kruížk, Oscillations and concentrations in sequences of gradients. ESAIM: COCV 14 (2008) 71–104. [Google Scholar]
  16. D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Ration. Mech. Anal. 115 (1991) 329–365. [Google Scholar]
  17. 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]
  18. D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59–90. [Google Scholar]
  19. J. Kristensen and F. Rindler, Characterization of generalized gradient Young measures generated by sequences in W1,1 and BV. Arch. Ration. Mech. Anal. 197 (2010) 539–598. [Google Scholar]
  20. S. Krömer, On the role of lower bounds in characterizations of weak lower semicontinuity of multiple integrals. Adv. Calc. Var. 3 (2010) 378–408. [Google Scholar]
  21. M. Kružík and M. Luskin, The computation of martensitic microstructure with piecewise laminates. J. Sci. Comput. 19 (2003) 293–308. [Google Scholar]
  22. M. Kružík and T. Roubcíek, On the measures of DiPerna and Majda. Math. Bohemica 122 (1997) 383–399. [Google Scholar]
  23. M. Kružík and T. Roubcíek, Optimization problems with concentration and oscillation effects: relaxation theory and numerical approximation. Numer. Funct. Anal. Optim. 20 (1999) 511–530. [Google Scholar]
  24. N.G. Meyers, Quasi-convexity and lower semicontinuity of multiple integrals of any order. Trans. Amer. Math. Soc. 119 (1965) 125–149. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Mielke and P. Sprenger, Quasiconvexity at the boundary and a simple variational formulation of Agmon’s condition. J. Elasticity 51 (1998) 23–41. [CrossRef] [MathSciNet] [Google Scholar]
  26. C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer, Berlin (1966). [Google Scholar]
  27. S. Müller, Higher integrability of determinants and weak convergence in L1. J. Reine Angew. Math. 412 (1990) 20–34. [MathSciNet] [Google Scholar]
  28. S. Müller, Variational models for microstructure and phase transisions, Lect. Notes Math., vol. 1713. Springer, Berlin (1999) 85–210. [CrossRef] [Google Scholar]
  29. P. Pedregal, Parametrized Measures and Variational Principles. Birkäuser, Basel (1997). [Google Scholar]
  30. T. Roubčíek, Relaxation in Optimization Theory and Variational Calculus. W. de Gruyter, Berlin (1997). [Google Scholar]
  31. T. Roubčíek and M. Kruıžk, Microstructure evolution model in micromagnetics. Zeit. Angew. Math. Phys. 55 (2004) 159–182. [CrossRef] [MathSciNet] [Google Scholar]
  32. T. Roubčíek and M. Kruıžk, Mesoscopical model for ferromagnets with isotropic hardening. Zeit. Angew. Math. Phys. 56 (2005) 107–135. [CrossRef] [MathSciNet] [Google Scholar]
  33. M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations. Commun. Partial Differ. Equ. 7 (1982) 959–1000. [CrossRef] [MathSciNet] [Google Scholar]
  34. M. Šilhavý, The Mechanics and Thermodynamics of Continuous Media. Springer, Berlin (1997). [Google Scholar]
  35. M. Šilhavý, Phase transitions with interfacial energy: Interface Null Lagrangians, Polyconvexity, and Existence, in IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, IUTAM Bookseries, vol. 21, edited by K. Hackl. Springer (2010) 233–244. [Google Scholar]
  36. P. Sprenger, Quasikonvexität am Rande und Null-Lagrange-Funktionen in der nichtkonvexen Variationsrechnung. Ph.D. thesis, Universität Hannover (1996). [Google Scholar]
  37. L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics, Heriott-Watt Symposium IV, Pitman Res. Notes Math., vol. 39, edited by R.J. Knops. (1979). [Google Scholar]
  38. 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, Proc. of the conference on multiscale problems in science and technology, held in Dubrovnik, Croatia, edited by N. Antonič et al. Springer, Berlin (2002). [Google Scholar]
  39. M. Valadier, Young measures, in Methods of Nonconvex Analysis, Lect. Notes Math., vol. 1446, edited by A. Cellina. Springer, Berlin (1990) 152–188. [Google Scholar]
  40. J. Warga, Optimal Control of Differential and Functional Equations. Academic Press, New York (1972). [Google Scholar]
  41. L.C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations. C. R. de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 30 (1937) 212–234. [Google Scholar]

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