On lower semicontinuity of multiple integrals

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1. [1] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. Zbl0565.49010
2. [2] L. Ambrosio, New lower semicontinuity results for integral functionals, Rend. Accad. Naz. Sci. XL Mem. Mat. Sci. Fis. Mat. Natur. 105 (1987), 1-42. Zbl0642.49007
3. [3] J. M. Ball, A version of the fundamental theorem for Young measures, in: PDE's and Continuum Models of Phase Transitions, M. Rascle, D. Serre and M. Slemrod (eds.), Lecture Notes in Phys. 344, Springer, Berlin, 1989. 
4. [4] J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403. Zbl0368.73040
5. [5] J. M. Ball and F. Murat, Remarks on Chacon's Biting Lemma, Proc. Amer. Math. Soc. 107 (1989), 655-663. Zbl0678.46023
6. [6] J. M. Ball and K. W. Zhang, Lower semicontinuity of multiple integrals and the Biting Lemma, Proc. Roy. Soc. Edinburgh Sect. A 114 (1990), 367-379. Zbl0716.49011
7. [7] B. Bojarski, Remarks on some geometric properties of Sobolev mappings, in: Functional Analysis and Related Topics, S. Koshi (ed.), World Scientific, Singapore, 1991, 65-76. Zbl0835.46025
8. [8] B. Bojarski and P. Hajłasz, Pointwise inequalities for Sobolev functions and some applications, Studia Math. 106 (1993), 77-92. Zbl0810.46030
9. [9] A. P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, ibid. 20 (1961), 171-225. Zbl0099.30103
10. [10] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, Berlin, 1989. Zbl0703.49001
11. [11] M. Esteban, A direct variational approach to Skyrme's model for meson fields, Comm. Math. Phys. 105 (1986), 571-591. Zbl0621.58035
12. [12] L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CMBS Regional Conf. Ser. in Math. 74, Amer. Math. Soc., Providence, R.I., 1990. 
13. [13] I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. Zbl0322.90046
14. [14] A. D. Ioffe, On lower semicontinuity of integral functionals, I, II, SIAM J. Control Optim. 15 (1977), 521-538, 991-1000. Zbl0361.46037
15. [15] D. Kinderlehrer and P. Pedregal, Characterisation of Young measures generated by gradients, Arch. Rational Mech. Anal. 115 (1991), 329-365. Zbl0754.49020
16. [16] D. Kinderlehrer and P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal. (to appear). Zbl0808.46046
17. [17] J. Kristensen, Lower semicontinuity of variational integrals, Ph.D. Thesis, Mathematical Institute, The Technical University of Denmark, 1994. 
18. [18] F. C. Liu, A Luzin type property of Sobolev functions, Indiana Univ. Math. J. 26 (1977), 645-651. Zbl0368.46036
19. [19] P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math. 51 (1985), 1-28. Zbl0573.49010
20. [20] N. G. Meyers, Quasi-convexity and lower semi-continuity of multiple variational functionals of any order, Trans. Amer. Math. Soc. 119 (1965), 125-149. Zbl0166.38501
21. [21] J. Michael and W. Ziemer, A Lusin type approximation of Sobolev functions by smooth functions, in: Contemp. Math. 42, Amer. Math. Soc., 1985, 135-167. Zbl0592.41031
22. [22] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. 
23. [23] M. Struwe, Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer, Berlin, 1990. 
24. [24] K. Zhang, Biting theorems for Jacobians and their applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), 345-365. Zbl0717.49012

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