Further remarks on the lower semicontinuity of polyconvex integrals
Pietro Celada; Gianni Dal Maso
Annales de l'I.H.P. Analyse non linéaire (1994)
- Volume: 11, Issue: 6, page 661-691
- ISSN: 0294-1449
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topCelada, Pietro, and Dal Maso, Gianni. "Further remarks on the lower semicontinuity of polyconvex integrals." Annales de l'I.H.P. Analyse non linéaire 11.6 (1994): 661-691. <http://eudml.org/doc/78348>.
@article{Celada1994,
author = {Celada, Pietro, Dal Maso, Gianni},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {lower semicontinuity; polyconvex integrals},
language = {eng},
number = {6},
pages = {661-691},
publisher = {Gauthier-Villars},
title = {Further remarks on the lower semicontinuity of polyconvex integrals},
url = {http://eudml.org/doc/78348},
volume = {11},
year = {1994},
}
TY - JOUR
AU - Celada, Pietro
AU - Dal Maso, Gianni
TI - Further remarks on the lower semicontinuity of polyconvex integrals
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 6
SP - 661
EP - 691
LA - eng
KW - lower semicontinuity; polyconvex integrals
UR - http://eudml.org/doc/78348
ER -
References
top- [1] E. Acerbi and G. DalMASO, New lower semicontinuity results for polyconvex integrals, Calc. Var. (to appear). Zbl0810.49014MR1385074
- [2] J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal., Vol. 58, 1984, pp. 225-253; Vol. 66, 1986, pp. 439. Zbl0549.46019MR759098
- [3] G. Buttazzo, Semicontinuity, relaxation and integral representation problems in the calculus of variations, Pitman Res. Notes in Math., Vol. 207, Longman, Harlow, 1989. Zbl0669.49005
- [4] B. Dacorogna, Direct methods in the calculus of variation, Springer-Verlag, Berlin, 1989. Zbl0703.49001MR990890
- [5] B. Dacorogna and P. Marcellini, Semicontinuité pour des intégrands polyconvexes sans continuité des déterminants, C. R. Acad. Sci. Paris, Sér. I, Vol. 311, 1990, pp. 393-396. Zbl0723.49007MR1071650
- [6] G. Dal Maso and C. Sbordone, Weak lower semicontinuity of policonvex integrals: a borderline case, Math. Z. (to appear). Zbl0822.49010MR1326990
- [7] H. Federer, Geometric measure theory, Springer-Verlag, Berlin, 1969. Zbl0176.00801MR257325
- [8] M. Giaquinta, G. Modica and J. Souček, Cartesian currents, weak diffeomorphisms and nonlinear elasticity, Arch. Rational Mech. Anal., Vol. 106, 1989, pp. 97-159; Vol. 109, 1990, pp. 385-392. Zbl0677.73014
- [9] M. Giaquinta, G. Modica and J. Souček, The Dirichlet integral for mappings between manifolds: cartesian currents and homology, Math. Ann, Vol. 294, 1992, pp. 325-386. Zbl0762.49018MR1183409
- [10] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Boston, 1984. Zbl0545.49018MR775682
- [11] C. Goffman and J. Serrin, Sublinear functions of measures and variational integrals, Duke Math. J., Vol. 31, 1964, pp. 159-178. Zbl0123.09804MR162902
- [12] J. Maly, Weak lower semicontinuity of polyconvex integrals, Proc. Roy. Soc., Edinburgh, Vol. 123A, 1993, pp. 681-691. Zbl0813.49017MR1237608
- [13] Yu.G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math. J., Vol. 101, 1961, pp. 139-167.
- [14] T. Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
- [15] L. Schwartz, Théorie des distributions, Hermann, Paris,1966. Zbl0149.09501MR209834
- [16] L.M. Simon, Lectures on geometric measure theory, Proc. of the Centre for Mathematical Analysis, Australian National University, Vol. 3, Canberra, 1983. Zbl0546.49019MR756417
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- E. Acerbi, G. Bouchitté, I. Fonseca, Relaxation of convex functionals : the gap problem
- Irene Fonseca, Giovanni Leoni, Stefan Müller, A-quasiconvexity : weak-star convergence and the gap
- M. A. Sychev, A new approach to Young measure theory, relaxation and convergence in energy
- Giovanni Leoni, On lower semicontinuity in the calculus of variations
- Irene Fonseca, Nicola Fusco, Paolo Marcellini, Topological degree, Jacobian determinants and relaxation
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