Relaxation of multiple integrals below the growth exponent
Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 3, p. 309-338
@article{AIHPC_1997__14_3_309_0,
     author = {Fonseca, Irene and Mal\'y, Jan},
     title = {Relaxation of multiple integrals below the growth exponent},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {3},
     year = {1997},
     pages = {309-338},
     zbl = {0868.49011},
     mrnumber = {1450951},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1997__14_3_309_0}
}
Fonseca, Irene; Malý, Jan. Relaxation of multiple integrals below the growth exponent. Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 3, pp. 309-338. http://www.numdam.org/item/AIHPC_1997__14_3_309_0/

[1] E. Acerbi and G. Dal MASO, New lower semicontinuity results for polyconvex integrals case, Preprint SISSA, Trieste, Vol. 52/M, 1993. | MR 1385074 | Zbl 0810.49014

[2] E. Acerbi and F. Fusco, Semicontinuity problems in the Calculus of variations, Arch. Rat. Mech. Anal., Vol. 86, 1984, pp. 125-145. | MR 751305 | Zbl 0565.49010

[3] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., Vol. 63 1977, pp. 337-403. | MR 475169 | Zbl 0368.73040

[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. | MR 759098 | Zbl 0549.46019

[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. | MR 1101308 | Zbl 0735.49008

[6] P. Celada and G. Dal Maso, Further remarks on the lower semicontinuity of polyconvex integrals, Ann. Inst. H. Poincaré (to appear). | Numdam | MR 1310627 | Zbl 0833.49013

[7] B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Math. Sciences 78, Springer-Verlag 1989. | MR 990890 | Zbl 0703.49001

[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. | MR 1071650 | Zbl 0723.49007

[9] G. Dal Maso and C. Sbordone, Weak lower semicontinuity of polyconvex integrals: a borderline case, Preprint SISSA, Trieste, Vol. 45, 1993. | MR 1326990 | Zbl 0822.49010

[10] I. Fonseca and J. Malý, On a class of relaxation functionals depending only on the jacobian, in preparation.

[11] I. Fonseca and P. Marcellini, Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal. (to appear). | MR 1630777 | Zbl 0915.49011

[12] N. Fusco and J.E. Hutchinson, A direct proof for lower semicontinuity of polyconvex functionals, Preprint 1994. | MR 1329439

[13] W. Gangbo, On the weak lower semicontinuity of energies with polyconvex integrands, J. Math. Pures et Appl., Vol. 73, 5, 1994. | MR 1300984 | Zbl 0829.49011

[14] P. Hajłasz, A note on weak approximation of minors, Ann. Inst. H. Poincaré (to appear). | Numdam | MR 1341410

[15] J. Malý, Weak lower semicontinuity of polyconvex integrals, Proc. Royal Soc. Edinburgh, Vol. 123A, 1993, pp. 681-691. | MR 1237608 | Zbl 0813.49017

[16] J. Malý, Weak lower semicontinuity of polyconvex and quasiconvex integrals, Vortragsreihe 1993, Bonn (to appear). | MR 1237608

[17] J. Malý, Lower semicontinuity of quasiconvex integrals, Manuscripta Math., Vol. 85, 1994, pp. 419-428. | MR 1305752 | Zbl 0862.49017

[18] P. Marcellini, Approximation of quasiconvex functions and lower semicontinuity of multiple integrals quasiconvex integrals, Manuscripta Math., Vol. 51, 1985, pp. 1-28. | MR 788671 | Zbl 0573.49010

[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. | Numdam | MR 868523 | Zbl 0609.49009

[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. | MR 188838 | Zbl 0166.38501

[21] C.B. Morrey, Quasiconvexity and the semicontinuity of multiple integrals, Pacific J. Math., Vol. 2, 1952, pp. 25-53. | MR 54865 | Zbl 0046.10803

[22] C.B. Morrey, Multiple integrals in the Calculus of Variations, Springer, Berlin 1966. | Zbl 0142.38701