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Issue
ESAIM: COCV
Volume 14, Number 1, January-March 2008
Page(s) 71 - 104
DOI https://doi.org/10.1051/cocv:2007051
Published online 21 September 2007
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal. 86 (1984) 125–145. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.J. Alibert and G. Bouchitté, Non-uniform integrability and generalized Young measures. J. Convex Anal. 4 (1997) 125–145. [Google Scholar]
  3. W. Allard, On the first variation of a varifold. Ann. Math. 95 (1972) 417–491. [CrossRef] [Google Scholar]
  4. F.J. Almgren Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure. Ann. Math. 87 (1968) 321–391. [CrossRef] [Google Scholar]
  5. 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]
  6. J.M Ball and F. Murat, Formula -quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  7. P. Billingsley, Probability and Measure. 3rd edn., John Wiley & Sons Ltd., Chichester (1995). [Google Scholar]
  8. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer, Berlin (1989). [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. 2nd edn., 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. Edinburgh 120A (1992) 95–115. [Google Scholar]
  14. I. Fonseca and S. Müller, P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 (1998) 736–756. [CrossRef] [MathSciNet] [Google Scholar]
  15. L. Greco, T. Iwaniec and U. Subramanian, Another approach to biting convergence of Jacobians. Illin. Journ. Math. 47 (2003) 815–830. [Google Scholar]
  16. M. de Guzmán, Differentiation of integrals in Formula , Lecture Notes in Math. 481. Springer, Berlin (1975). [Google Scholar]
  17. O.M Hafsa, J.-P. Mandallena and G. Michaille, Homogenization of periodic nonconvex integral functionals in terms of Young measures. ESAIM: COCV 12 (2006) 35–51. [CrossRef] [EDP Sciences] [Google Scholar]
  18. A. Kałamajska, On lower semicontinuity of multiple integrals. Coll. Math. 74 (1997) 71–78. [Google Scholar]
  19. A. Kałamajska, On Young measures controlling discontinuous functions. J. Conv. Anal. 13 (2006) 177–192. [Google Scholar]
  20. A. Kałamajska and M. Kružík, On weak lower semicontinuity of integral functionals along concentrating sequences (in preparation). [Google Scholar]
  21. D. Kinderlehrer and P. Pedregal, Characterization of Young measures generated by gradients. Arch. Rat. Mech.Anal. 115 (1991) 329–365. [Google Scholar]
  22. D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59–90. [Google Scholar]
  23. J. Kristensen, Finite functionals and Young measures generated by gradients of Sobolev functions. Mat-report 1994-34, Math. Institute, Technical University of Denmark (1994). [Google Scholar]
  24. J. Kristensen, Lower semicontinuity in spaces of weakly differentiable functions. Math. Ann. 313 (1999) 653–710. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Kružík and T. Roubíček, On the measures of DiPerna and Majda. Mathematica Bohemica 122 (1997) 383–399. [MathSciNet] [Google Scholar]
  26. 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]
  27. C. Licht, G. Michaille and S. Pagano, A model of elastic adhesive bonded joints through oscillation-concentration measures. Prépublication of the Institut de Mathématiques et de Modélisation de Montpellier, UMR-CNRS 5149. [Google Scholar]
  28. P. Marcellini, Approximation of quasiconvex functions and lower semicontinuity of multiple integrals. Manuscripta Math. 51 (1985) 1–28. [Google Scholar]
  29. V.G. Mazja, Sobolev Spaces. Springer, Berlin (1985). [Google Scholar]
  30. N.G. Meyers, Quasi-convexity and lower semicontinuity of multiple integrals of any order. Trans. Am. Math. Soc. 119 (1965) 125–149. [Google Scholar]
  31. C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer, Berlin (1966). [Google Scholar]
  32. S. Müller, Variational models for microstructure and phase transisions. Lecture Notes in Mathematics 1713 (1999) 85–210. [Google Scholar]
  33. P. Pedregal, Parametrized Measures and Variational Principles. Birkäuser, Basel (1997). [Google Scholar]
  34. Yu.G. Reshetnyak, The generalized derivatives and the a.e. differentiability. Mat. Sb. 75 (1968) 323–334 (in Russian). [MathSciNet] [Google Scholar]
  35. Yu.G. Reshetnyak, Weak convergence and completely additive vector functions on a set. Sibirsk. Mat. Zh. 9 (1968) 1039–1045. [Google Scholar]
  36. T. Roubíček, Relaxation in Optimization Theory and Variational Calculus. W. de Gruyter, Berlin (1997). [Google Scholar]
  37. M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations. Comm. Part. Diff. Equa. 7 (1982) 959–1000. [Google Scholar]
  38. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton university Press, Princeton (1970). [Google Scholar]
  39. 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 Math. 39, San Francisco (1979). [Google Scholar]
  40. 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 et al. 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]
  41. M. Valadier, Young measures, in Methods of Nonconvex Analysis, A. Cellina Ed., Lect. Notes Math. 1446, Springer, Berlin (1990) 152–188. [Google Scholar]
  42. J. Warga, Optimal Control of Differential and Functional Equations. Academic Press, New York (1972). [Google Scholar]
  43. 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]

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