Relaxation of multiple integrals below the growth exponent

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1. [1] E. Acerbi and G. DalMASO, New lower semicontinuity results for polyconvex integrals case, Preprint SISSA, Trieste, Vol. 52/M, 1993. Zbl0810.49014MR1385074
2. [2] E. Acerbi and F. Fusco, Semicontinuity problems in the Calculus of variations, Arch. Rat. Mech. Anal., Vol. 86, 1984, pp. 125-145. Zbl0565.49010MR751305
3. [3] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., Vol. 631977, pp. 337-403. Zbl0368.73040MR475169
4. [4] J.M. Ball and F. Murat, W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal., Vol. 58, 1984, pp. 225-253. Zbl0549.46019MR759098
5. [5] L. Carbone and R. De Arcangelis, Further results on Γ-convergence and lower semicontinuity of integral functionals depending on vector-valued functions, Richerche Mat., Vol. 39, 1990, pp. 99-129. Zbl0735.49008MR1101308
6. [6] P. Celada and G. Dal Maso, Further remarks on the lower semicontinuity of polyconvex integrals, Ann. Inst. H. Poincaré (to appear). Zbl0833.49013MR1310627
7. [7] B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Math. Sciences 78, Springer-Verlag1989. Zbl0703.49001MR990890
8. [8] B. Dacorogna and P. Marcellini, Semicontinuité pour des intégrandes polyconvexes sans continuité des determinants, C. R. Acad. Sci. Paris Sér. I Math., Vol. 311, 6, 1990, pp. 393-396. Zbl0723.49007MR1071650
9. [9] G. Dal Maso and C. Sbordone, Weak lower semicontinuity of polyconvex integrals: a borderline case, Preprint SISSA, Trieste, Vol. 45, 1993. Zbl0822.49010MR1326990
10. [10] I. Fonseca and J. Malý, On a class of relaxation functionals depending only on the jacobian, in preparation. 
11. [11] I. Fonseca and P. Marcellini, Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal. (to appear). Zbl0915.49011MR1630777
12. [12] N. Fusco and J.E. Hutchinson, A direct proof for lower semicontinuity of polyconvex functionals, Preprint1994. Zbl0874.49015MR1329439
13. [13] W. Gangbo, On the weak lower semicontinuity of energies with polyconvex integrands, J. Math. Pures et Appl., Vol. 73, 5, 1994. Zbl0829.49011MR1300984
14. [14] P. Hajłasz, A note on weak approximation of minors, Ann. Inst. H. Poincaré (to appear). Zbl0910.49025MR1341410
15. [15] J. Malý, Weak lower semicontinuity of polyconvex integrals, Proc. Royal Soc. Edinburgh, Vol. 123A, 1993, pp. 681-691. Zbl0813.49017MR1237608
16. [16] J. Malý, Weak lower semicontinuity of polyconvex and quasiconvex integrals, Vortragsreihe1993, Bonn (to appear). Zbl0813.49017MR1237608
17. [17] J. Malý, Lower semicontinuity of quasiconvex integrals, Manuscripta Math., Vol. 85, 1994, pp. 419-428. Zbl0862.49017MR1305752
18. [18] P. Marcellini, Approximation of quasiconvex functions and lower semicontinuity of multiple integrals quasiconvex integrals, Manuscripta Math., Vol. 51, 1985, pp. 1-28. Zbl0573.49010MR788671
19. [19] P. Marcellini, On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré, Analyse non Linéaire, Vol. 3, 1986, pp. 391-409. Zbl0609.49009MR868523
20. [20] N.G. Meyers, Quasiconvexity and the semicontinuity of multiple variational integrals of any order, Trans. Amer. Math. Soc., Vol. 119, 1965, pp. 125-149. Zbl0166.38501MR188838
21. [21] C.B. Morrey, Quasiconvexity and the semicontinuity of multiple integrals, Pacific J. Math., Vol. 2, 1952, pp. 25-53. Zbl0046.10803MR54865
22. [22] C.B. Morrey, Multiple integrals in the Calculus of Variations, Springer, Berlin1966. Zbl0142.38701

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