@article{AIHPC_2004__21_2_209_0, author = {Fonseca, Irene and Leoni, Giovanni and M\"uller, Stefan}, title = {A-quasiconvexity : weak-star convergence and the gap}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {21}, year = {2004}, pages = {209-236}, doi = {10.1016/j.anihpc.2003.01.003}, mrnumber = {2021666}, zbl = {1064.49016}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_2_209_0} }
Fonseca, Irene; Leoni, Giovanni; Müller, Stefan. A-quasiconvexity : weak-star convergence and the gap. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 209-236. doi : 10.1016/j.anihpc.2003.01.003. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_2_209_0/
[1] E. Acerbi, G. Bouchitté, I. Fonseca, Relaxation of convex functionals and the Lavrentiev phenomenon, submitted for publication.
[2] Semicontinuity and relaxation for integrals depending on vector valued functions, J. Math. Pures Appl. 62 (1983) 371-387. | MR 735930 | Zbl 0481.49013
, , ,[3] New lower semicontinuity results for polyconvex integrals case, Calc. Var. 2 (1994) 329-372. | MR 1385074 | Zbl 0810.49014
, ,[4] Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984) 125-145. | MR 751305 | Zbl 0565.49010
, ,[5] Functions of Bounded Variation and Free Discontinuity Problems, Mathematical Monographs, Oxford University Press, 2000. | MR 1857292 | Zbl 0957.49001
, , ,[6] On the relaxation in BV(Ω;Rm) of quasi-convex integrals, J. Funct. Anal. 109 (1992) 76-97. | Zbl 0769.49009
, ,[7] Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403. | MR 475169 | Zbl 0368.73040
,[8] W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984) 225-253. | MR 759098 | Zbl 0549.46019
, ,[9] Relaxation of multiple integrals below the growth exponent, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 463-479. | MR 1632814 | Zbl 0907.49008
, , ,[10] A-quasiconvexity: relaxation and homogenization, ESAIM:COCV 5 (2000) 539-577. | Numdam | MR 1799330 | Zbl 0971.35010
, , ,[11] Sobolev Spaces on Domains, Teuber, Stuttgart, 1998. | MR 1622690 | Zbl 0893.46024
,[12] Further remarks on the lower semicontinuity of polyconvex integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994) 661-691. | Numdam | MR 1310627 | Zbl 0833.49013
, ,[13] Weak Continuity and Weak Lower Semicontinuity for Nonlinear Functionals, Lecture Notes in Mathem., vol. 922, Springer, Berlin, 1982. | MR 658130 | Zbl 0484.46041
,[14] Direct Methods in the Calculus of Variations, Springer, New York, 1989. | MR 990890 | Zbl 0703.49001
,[15] Weak lower semicontinuity of polyconvex integrals: a borderline case, Math. Z. 218 (1995) 603-609. | MR 1326990 | Zbl 0822.49010
, ,[16] Energy minimizers for large ferromagnetic bodies, Arch. Rational Mech. Anal. 125 (1993) 99-143. | MR 1245068 | Zbl 0811.49030
,[17] Fonctions à hessien borné, Ann. Inst. Fourier 34 (1984) 155-190. | Numdam | MR 746501 | Zbl 0525.46020
,[18] L. Esposito, F. Leonetti, G. Mingione, Sharp regularity for functionals with (p,q) growth, Preprint. | MR 2076158
[19] L. Esposito, G. Mingione, Relaxation results for higher order integrals below the natural growth exponent, Differential Integral Equations, submitted for publication. | MR 1893841 | Zbl 1030.49013
[20] I. Fonseca, G. Leoni, J. Malý, Weak continuity and lower semicontinuity results for determinants, in preparation.
[21] Relaxation of multiple integrals below the growth exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 308-338. | Numdam | MR 1450951 | Zbl 0868.49011
, ,[22] Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal. 7 (1997) 57-81. | MR 1630777 | Zbl 0915.49011
, ,[23] Quasiconvex integrands and lower semicontinuity in L1, SIAM J. Math. Anal. 23 (1992) 1081-1098. | MR 1177778 | Zbl 0764.49012
, ,[24] Relaxation of quasiconvex functionals in BV(Ω, Rp) for integrands f(x,u,∇u), Arch. Rational Mech. Anal. 123 (1993) 1-49. | Zbl 0788.49039
, ,[25] A-quasiconvexity, lower semicontinuity and Young measures, SIAM J. Math. Anal. 30 (1999) 1355-1390. | MR 1718306 | Zbl 0940.49014
, ,[26] Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Padova 27 (1957) 283-305. | Numdam | MR 102739 | Zbl 0087.10902
,[27] On the weak lower semicontinuity of energies with polyconvex integrands, J. Math. Pures Appl. 73 (1994) 455-469. | MR 1300984 | Zbl 0829.49011
,[28] Lower semicontinuity for quasiconvex integrals of higher order, Nonlinear Differential Equations Appl. 6 (1999) 227-246. | MR 1691445 | Zbl 0930.35059
, ,[29] Lower semicontinuity of quasi-convex integrands in BV, Calc. Var. 7 (1998) 249-261. | MR 1651438 | Zbl 0915.49007
,[30] Weak lower semicontinuity of polyconvex integrals, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 681-691. | MR 1237608 | Zbl 0813.49017
,[31] Lower semicontinuity of quasiconvex integrals, Manuscripta Math. 85 (1994) 419-428. | MR 1305752 | Zbl 0862.49017
,[32] Approximation of quasiconvex functions and lower semicontinuity of multiple integrals quasiconvex integrals, Manuscripta Math. 51 (1985) 1-28. | MR 788671 | Zbl 0573.49010
,[33] On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 391-409. | Numdam | MR 868523 | Zbl 0609.49009
,[34] Sobolev Spaces, Springer, Berlin, 1985. | MR 817985
,[35] Quasi-convexity and lower semi-continuity of multiple variational integrals of any order, Trans. Amer. Math. Soc. 119 (1965) 125-149. | MR 188838 | Zbl 0166.38501
,[36] Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. | MR 202511 | Zbl 0142.38701
,[37] Compacité par compensation : condition necessaire et suffisante de continuité faible sous une hypothése de rang constant, Ann. Sc. Norm. Sup. Pisa 8 (4) (1981) 68-102. | Numdam | MR 616901 | Zbl 0464.46034
,[38] Parametrized Measures and Variational Principles, Birkhäuser, Boston, 1997. | MR 1452107 | Zbl 0879.49017
,[39] P. Santos, E. Zappale, in preparation.
[40] On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc. 161 (1961) 139-167. | MR 138018 | Zbl 0102.04601
,[41] Harmonic Analysis, Princeton University Press, 1993. | MR 1232192 | Zbl 0821.42001
,[42] Compensated compactness and applications to partial differential equations, in: (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. IV, Res. Notes Math., vol. 39, Pitman, 1979, pp. 136-212. | MR 584398 | Zbl 0437.35004
,[43] The compensated compactness method applied to systems of conservation laws, in: (Ed.), Systems of Nonlinear Partial Differential Eq., Riedel, 1983. | MR 725524 | Zbl 0536.35003
,[44] Étude des oscillations dans les équations aux dérivées partielles nonlinéaires, in: Lecture Notes in Phys., vol. 195, Springer, Berlin, 1984, pp. 384-412. | MR 755737 | Zbl 0595.35012
,[45] H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 193-230. | MR 1069518 | Zbl 0774.35008
,[46] On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures, in: , , (Eds.), Developments in Partial Differential Equations and Applications to Mathematical Physics, Plenum, New York, 1991. | MR 1213932 | Zbl 0897.35010
,[47] Some remarks on separately convex functions, in: , , , (Eds.), Microstructure and Phase Transitions, IMA Vol. Math. Appl., vol. 54, Springer, Berlin, 1993, pp. 191-204. | MR 1320538 | Zbl 0823.26008
,[48] On Lavrentiev's phenomenon, Russian J. Math. Phys. 3 (1995) 249-269. | MR 1350506 | Zbl 0910.49020
,[49] On some variational problems, Russian J. Math. Phys. 5 (1997) 105-116. | MR 1486765 | Zbl 0917.49006
,