@article{AIHPC_2003__20_3_359_0, author = {Acerbi, E. and Bouchitt\'e, G. and Fonseca, I.}, title = {Relaxation of convex functionals : the gap problem}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {359--390}, publisher = {Elsevier}, volume = {20}, number = {3}, year = {2003}, doi = {10.1016/S0294-1449(02)00017-3}, mrnumber = {1972867}, zbl = {1025.49012}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S0294-1449(02)00017-3/} }
TY - JOUR AU - Acerbi, E. AU - Bouchitté, G. AU - Fonseca, I. TI - Relaxation of convex functionals : the gap problem JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 359 EP - 390 VL - 20 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S0294-1449(02)00017-3/ DO - 10.1016/S0294-1449(02)00017-3 LA - en ID - AIHPC_2003__20_3_359_0 ER -
%0 Journal Article %A Acerbi, E. %A Bouchitté, G. %A Fonseca, I. %T Relaxation of convex functionals : the gap problem %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 359-390 %V 20 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S0294-1449(02)00017-3/ %R 10.1016/S0294-1449(02)00017-3 %G en %F AIHPC_2003__20_3_359_0
Acerbi, E.; Bouchitté, G.; Fonseca, I. Relaxation of convex functionals : the gap problem. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 3, pp. 359-390. doi : 10.1016/S0294-1449(02)00017-3. http://www.numdam.org/articles/10.1016/S0294-1449(02)00017-3/
[1] New lower semicontinuity results for polyconvex integrals, Cal. Var. 2 (1994) 329-337. | MR | Zbl
, ,[2] Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984) 125-145. | MR | Zbl
, ,[3] Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403. | MR | Zbl
,[4] W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984) 225-253. | MR | Zbl
, ,[5] G. Bouchitté, I. Fonseca, G. Leoni, L. Mascarenhas, A global method for relaxation in W1,p and in SBVp, To appear in Arch. Rational Mech. Anal. | MR | Zbl
[6] The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 463-479. | MR | Zbl
, , ,[7] A global method for relaxation, Arch. Rational Mech. Anal. 144 (1998) 1-46. | MR | Zbl
, , ,[8] Further results on Γ-convergence and lower semicontinuity of integral functionals depending on vector-valued functions, Ricerche Mat. 39 (1990) 99-129. | Zbl
, ,[9] Further remarks on the lower semicontinuity of polyconvex integrals, Ann. Inst. Henri Poincaré Anal. Non Linéaire 11 (1994) 661-691. | Numdam | MR | Zbl
, ,[10] Direct Methods in the Calculus of Variations, Applied Math. Sciences, 78, Springer-Verlag, 1989. | MR | Zbl
,[11] Semicontinuité pour des intégrandes polyconvexes sans continuité des determinants, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 393-396. | MR | Zbl
, ,[12] Weak lower semicontinuity of polyconvex integrals: a borderline case, Math. Z. 218 (1995) 603-609. | MR | Zbl
, ,[13] Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. | MR | Zbl
, ,[14] A class of De Giorgi type and Hölder continuity, Nonlinear Anal. TMA 36 (A) (1999) 295-318. | MR | Zbl
, ,[15] Relaxation of multiple integrals below the growth exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 309-338. | Numdam | MR | Zbl
, ,[16] Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal. 7 (1997) 57-81. | MR | Zbl
, ,[17] A direct proof for lower semicontinuity of polyconvex functionals, Manuscripta Math. 85 (1995) 35-50. | MR | Zbl
, ,[18] On the weak lower semicontinuity of energies with polyconvex integrands, J. Math. Pures Appl. 73 (1994) 455-469. | MR | Zbl
,[19] On lower semicontinuity of integral functionals I, SIAM J. Control Optim. 15 (1977) 521-538. | MR | Zbl
,[20] The formation of filamentary voids in solids, J. Mech. Phys. Solids 39 (1991) 783-813. | MR | Zbl
, ,[21] The formation of filamentary voids in solids, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 681-691.
, ,[22] J. Malý, Weak lower semicontinuity of polyconvex and quasiconvex integrals, Preprint, Vortragsreihe, Bonn, 1993. | MR
[23] Lower semicontinuity of quasiconvex integrals, Manuscripta Math. 85 (1994) 419-428. | MR | Zbl
,[24] Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math. 51 (1985) 1-28. | MR | Zbl
,[25] On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 391-409. | Numdam | MR | Zbl
,[26] Multiple integrals in the Calculus of Variations, Springer, Berlin, 1966. | MR | Zbl
,[27] An existence theory for nonlinear elasticity that allows for cavitation, Arch. Rational Mech. Anal. 131 (1995) 1-66. | MR | Zbl
, ,[28] On cavitation and degenerate cavitation under internal hydrostatic pressure, Roy. Soc. London Proc. Ser. A Math. Phys. Eng. Sci. 455 (1999) 3645-3664. | MR | Zbl
,[29] On Lavrentiev's phenomenon, Russian J. Math. Phys. 3 (1995) 249-269. | MR | Zbl
,[30] On some variational problems, Russian J. Math. Phys. 5 (1997) 105-116. | MR | Zbl
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