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

How to cite

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Celada, 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

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  1. [1] E. Acerbi and G. DalMASO, New lower semicontinuity results for polyconvex integrals, Calc. Var. (to appear). Zbl0810.49014MR1385074
  2. [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. [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. [4] B. Dacorogna, Direct methods in the calculus of variation, Springer-Verlag, Berlin, 1989. Zbl0703.49001MR990890
  5. [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. [6] G. Dal Maso and C. Sbordone, Weak lower semicontinuity of policonvex integrals: a borderline case, Math. Z. (to appear). Zbl0822.49010MR1326990
  7. [7] H. Federer, Geometric measure theory, Springer-Verlag, Berlin, 1969. Zbl0176.00801MR257325
  8. [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. [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. [10] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Boston, 1984. Zbl0545.49018MR775682
  11. [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. [12] J. Maly, Weak lower semicontinuity of polyconvex integrals, Proc. Roy. Soc., Edinburgh, Vol. 123A, 1993, pp. 681-691. Zbl0813.49017MR1237608
  13. [13] Yu.G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math. J., Vol. 101, 1961, pp. 139-167. 
  14. [14] T. Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
  15. [15] L. Schwartz, Théorie des distributions, Hermann, Paris,1966. Zbl0149.09501MR209834
  16. [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

Citations in EuDML Documents

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  1. Irene Fonseca, Jan Malý, Relaxation of multiple integrals below the growth exponent
  2. Luigi Ambrosio, Francesco Ghiraldin, Compactness of Special Functions of Bounded Higher Variation
  3. E. Acerbi, G. Bouchitté, I. Fonseca, Relaxation of convex functionals : the gap problem
  4. Irene Fonseca, Giovanni Leoni, Stefan Müller, A-quasiconvexity : weak-star convergence and the gap
  5. M. A. Sychev, A new approach to Young measure theory, relaxation and convergence in energy
  6. Giovanni Leoni, On lower semicontinuity in the calculus of variations
  7. Irene Fonseca, Nicola Fusco, Paolo Marcellini, Topological degree, Jacobian determinants and relaxation

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