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.
@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},
     pages = {309--338},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {3},
     year = {1997},
     mrnumber = {1450951},
     zbl = {0868.49011},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1997__14_3_309_0/}
}
TY  - JOUR
AU  - Fonseca, Irene
AU  - Malý, Jan
TI  - Relaxation of multiple integrals below the growth exponent
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1997
SP  - 309
EP  - 338
VL  - 14
IS  - 3
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1997__14_3_309_0/
LA  - en
ID  - AIHPC_1997__14_3_309_0
ER  - 
%0 Journal Article
%A Fonseca, Irene
%A Malý, Jan
%T Relaxation of multiple integrals below the growth exponent
%J Annales de l'I.H.P. Analyse non linéaire
%D 1997
%P 309-338
%V 14
%N 3
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1997__14_3_309_0/
%G en
%F 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://archive.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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

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

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