Relaxation theorems in nonlinear elasticity

Omar Anza Hafsa; Jean-Philippe Mandallena

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 1, page 135-148
  • ISSN: 0294-1449

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Anza Hafsa, Omar, and Mandallena, Jean-Philippe. "Relaxation theorems in nonlinear elasticity." Annales de l'I.H.P. Analyse non linéaire 25.1 (2008): 135-148. <http://eudml.org/doc/78776>.

@article{AnzaHafsa2008,
author = {Anza Hafsa, Omar, Mandallena, Jean-Philippe},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {determinant condition; infinite energy},
language = {eng},
number = {1},
pages = {135-148},
publisher = {Elsevier},
title = {Relaxation theorems in nonlinear elasticity},
url = {http://eudml.org/doc/78776},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Anza Hafsa, Omar
AU - Mandallena, Jean-Philippe
TI - Relaxation theorems in nonlinear elasticity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 1
SP - 135
EP - 148
LA - eng
KW - determinant condition; infinite energy
UR - http://eudml.org/doc/78776
ER -

References

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  1. [1] Anza Hafsa O., Mandallena J.-P., Relaxation of variational problems in two-dimensional nonlinear elasticity, Ann. Mat. Pura Appl.186 (2007) 187-198. Zbl1232.49015MR2263896
  2. [2] Anza Hafsa O., Mandallena J.-P., The nonlinear membrane energy: variational derivation under the constraint “ det ∇ u ≠ 0 ”, J. Math. Pures Appl.86 (2006) 100-115. Zbl1114.35003MR2247453
  3. [3] O. Anza Hafsa, J.-P. Mandallena, The nonlinear membrane energy: variational derivation under the constraint “ det ∇ u g t ; 0 ”, submitted for publication. Zbl1148.35004
  4. [4] Ball J.M., Murat F., W 1 , p -quasiconvexity and variational problems for multiple integrals, J. Funct. Anal.58 (1984) 225-253. Zbl0549.46019MR759098
  5. [5] Ben Belgacem H., Relaxation of singular functionals defined on Sobolev spaces, ESAIM Control Optimal Calc. Var.5 (2000) 71-85. Zbl0936.49008MR1745687
  6. [6] Buttazzo G., Semicontinuity, Relaxation and Integral Representation Problems in the Calculus of Variations, Pitman Res., Notes Math. Ser., vol. 207, Longman, Harlow, 1989. Zbl0669.49005
  7. [7] Carbone L., De Arcangelis R., Unbounded Functionals in the Calculus of Variations: Representation, Relaxation and Homogenization, Chapman & Hall/CRC, 2001. Zbl1002.49018MR1910459
  8. [8] Dacorogna B., Quasiconvexity and relaxation of nonconvex problems in the calculus of variations, J. Funct. Anal.46 (1982) 102-118. Zbl0547.49003MR654467
  9. [9] Dacorogna B., Direct Methods in the Calculus of Variations, Springer, Berlin, 1989. Zbl0703.49001MR990890
  10. [10] Ekeland I., Temam R., Analyse convexe et problèmes variationnels, Dunod, Gauthier-Villars, Paris, 1974. Zbl0281.49001MR463993
  11. [11] Fonseca I., The lower quasiconvex envelope of the stored energy function for an elastic crystal, J. Math. Pures Appl.67 (1988) 175-195. Zbl0718.73075MR949107
  12. [12] Marsden J.E., Hughes T.J.R., Mathematical Foundations of Elasticity, Prentice-Hall, 1983. Zbl0545.73031
  13. [13] Morrey C.B., Quasiconvexity and lower semicontinuity of multiple integrals, Pacific J. Math.2 (1952) 25-53. Zbl0046.10803MR54865

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