logo AFST
Lower semicontinuity of a class of multiple integrals below the growth exponent
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 2, pp. 299-311.
@article{AFST_2001_6_10_2_299_0,
     author = {Flavia Giannetti and Anna Verde},
     title = {Lower semicontinuity of a class of multiple integrals below the growth exponent},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {299--311},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {Ser. 6, 10},
     number = {2},
     year = {2001},
     zbl = {1017.49016},
     mrnumber = {1896184},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2001_6_10_2_299_0/}
}
TY  - JOUR
AU  - Flavia Giannetti
AU  - Anna Verde
TI  - Lower semicontinuity of a class of multiple integrals below the growth exponent
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2001
SP  - 299
EP  - 311
VL  - 10
IS  - 2
PB  - Université Paul Sabatier. Faculté des sciences
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/item/AFST_2001_6_10_2_299_0/
LA  - en
ID  - AFST_2001_6_10_2_299_0
ER  - 
%0 Journal Article
%A Flavia Giannetti
%A Anna Verde
%T Lower semicontinuity of a class of multiple integrals below the growth exponent
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2001
%P 299-311
%V 10
%N 2
%I Université Paul Sabatier. Faculté des sciences
%C Toulouse
%U https://afst.centre-mersenne.org/item/AFST_2001_6_10_2_299_0/
%G en
%F AFST_2001_6_10_2_299_0
Flavia Giannetti; Anna Verde. Lower semicontinuity of a class of multiple integrals below the growth exponent. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 2, pp. 299-311. https://afst.centre-mersenne.org/item/AFST_2001_6_10_2_299_0/

[1] Acerbi (E.), Dal Maso (G.). - New lower semicontinuity results for polyconvex integrals, Calc. Var. Partial Differential Equations 2 (1994), no.3, 329-371. | MR | Zbl

[2] Acerbi (E.), Fusco (N.). - Semicontinuity problems in the Calculus of Variations, Arch. Rat. Mech. Anal. 86 (1984), 125-145. | MR | Zbl

[3] Ball (J.M.). - Convexity conditions and existence theorems in nonlinear elsticity, Arch. Rational Mech. Anal. 63 (1977), 337-403. | MR | Zbl

[4] Ball (J.M.), Murat (F.). - W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225-253. | MR | Zbl

[5] Dacorogna (B.). - Direct Methods in the Calculus of Variations, Springer Verlag, Berlin (1989). | MR | Zbl

[6] Dacorogna (B.), Marcellini (P.). - Semicontinuité pour des intégrandes polyconvexes sans continuité des déterminants, C.R. Acad. Sci. Paris, 311 (1990), 393-396. | MR | Zbl

[7] Dal Maso (G.), Sbordone (C.). - Weak lower semicontinuity of polyconvex integrals : a borderline case, Math. Z. 218 (1995), no.4, 603-609. | MR | Zbl

[8] Ekeland (I.), Temam (R.). - Convex Analysis and Variational Problems, North-Holland, New York (1976). | MR | Zbl

[9] Evans (L.C.), Gariepy (R.F.). - Measure theory and fine properties of functions,Studies in Advanced Maths.CRC Press 1992. | MR | Zbl

[10] Fonseca (I.), Müller (S.). - A-quasiconvexity, lower semicontinuity and Young measures, SIAM J. Math. Anal. 30 (1999), n.6, 1355-1390. | MR | Zbl

[11] Fonseca (I.), Malý (J.). - Relaxation of multiple integrals below the growth exponents, Ann. Inst. H. Poincaré 14, n.3 (1997), 309-338. | EuDML | Numdam | MR | Zbl

[12] Fonseca (I.), Marcellini (P.). - Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal. 7 (1997), no.1, 57-81. | MR | Zbl

[13] Fusco (N.), Hutchinson (J.E.). - A direct proof for lower semicontinuity of polyconvex functionals, Manu- scripta Math. 87 (1995), 35-50. | EuDML | MR | Zbl

[14] Gangbo (W.). - On the weak lower semicontinuity of energies with polyconvex integrands J. Math. Pures et Appl. 73 (1994), 455-469. | MR | Zbl

[15] Giannetti (F.), Verde (A.). - Variational Integrals for Elliptic Complexes, Studia Math. 140 (2000), no.1, 79-98. | EuDML | MR | Zbl

[16] Iwaniec (T.), Sbordone (C.). - Quasiharmonic Fields, Ann. Inst. H. Poincaré Anal. Non Linéaire 18, n. 5 (2001), 519-572. | EuDML | Numdam | MR | Zbl

[17] Kristensen (J.). - Finite Functionals and Young Measures Generated by Gradients of Sobolev Functions , Mat- Report 1994-34, Mathematical Institute, Technical University of Denmark, Lyngby, Denmark,1994.

[18] Malý (J.). - Weak lower semicontinuity of polyconvex integrands, Proc. Royal Soc. Edin. 123A (1993), 681-691. | MR | Zbl

[19] Marcellini (P.). - On the definition and lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré (1986), 391-409. | EuDML | Numdam | MR | Zbl

[20] Meyers (N.G.). - Quasiconvexity and the semicontinuity of multiple integrals of any order, Trans. Amer. Math. Soc. 119 (1965), 125-149. | MR | Zbl

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

[22] Morrey (C.B.). - Multiple integrals in the calculus of variations Die Grund. der Math. Wiss. 130, Springer Verlag, Heidelberg and New York, 1966. | MR | Zbl