Lower semicontinuity of multiple integrals and convergent integrands

Li Zhiping

ESAIM: Control, Optimisation and Calculus of Variations (1996)

  • Volume: 1, page 169-189
  • ISSN: 1292-8119

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Zhiping, Li. "Lower semicontinuity of multiple integrals and convergent integrands." ESAIM: Control, Optimisation and Calculus of Variations 1 (1996): 169-189. <http://eudml.org/doc/90493>.

@article{Zhiping1996,
author = {Zhiping, Li},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {lower semicontinuity; convergent integrands; lower precompactness; weakly precompact; quasiconvex; integral functional},
language = {eng},
pages = {169-189},
publisher = {EDP Sciences},
title = {Lower semicontinuity of multiple integrals and convergent integrands},
url = {http://eudml.org/doc/90493},
volume = {1},
year = {1996},
}

TY - JOUR
AU - Zhiping, Li
TI - Lower semicontinuity of multiple integrals and convergent integrands
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1996
PB - EDP Sciences
VL - 1
SP - 169
EP - 189
LA - eng
KW - lower semicontinuity; convergent integrands; lower precompactness; weakly precompact; quasiconvex; integral functional
UR - http://eudml.org/doc/90493
ER -

References

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  1. [1] Z.-P. Li: Numerical methods for Computing singular minimizers, Numer. Math., 71, 1995, 317-330. Zbl0833.65062MR1347572
  2. [2] A. D. Ioffe: On lower semicontinuity of integral functionals, SIAM J. Control Optim., 15, 1977, 521-538. Zbl0361.46037MR637234
  3. [3] J. Diestel and J. J. Uhl, Jr: Vector Measures, Ameri. Math. Society, Providence, Rhode Island, 1977. Zbl0369.46039MR453964
  4. [4] C. B. Morrey: Multiple Integrals in the Calculus of Variations, Springer, New York, 1966. Zbl0142.38701MR202511
  5. [5] E. Acerbi and N. Fusco: Semicontinuity problems in the calculus of variations, Arch. Rat. Mech. Anal., 86, 1984, 125-145. Zbl0565.49010MR751305
  6. [6] J. M. Ball and K.-W. Zhang: Lower semicontinuity of multiple integrals and the biting lemma, Proc. R. Soc. Edinburgh, 114A, 1990, 367-379. Zbl0716.49011MR1055554
  7. [7] J. K. Brooks and K. V. Chacon: Continuity and compactness of measures, Adv. in Math., 37, 1980, 16-26. Zbl0463.28003MR585896
  8. [8] J. M. Ball and F. Murat: Remarks on Chacon's biting lemma, Proc. Amer. Math. Soc., 107, 1989, 655-663. Zbl0678.46023MR984807
  9. [9] F. Murat: A survey on compensated compactness, in Contributions to Modern Calculus of variations, L. Cesari. ed., Longman, Harlow, 1987. MR894077
  10. [10] L. Tartar: The compensated method applied to Systems of conservation laws, in Systems of Nonlinear Partial Differential Equations, NATO ASI Series, Vol. C 111, J.M. Ball ed., 263-285, Reidel, Amstertam, 1982. Zbl0536.35003MR725524
  11. [11] Y.G. Reshetnyak: General theorems on semicontinuity and on convergence with a functional, Siberian Math. J., 8, 1967, 69-85. Zbl0179.20902
  12. [12] Z.-P. Li: A theorem on lower semicontinuity of integral functionals, Proc. R. Soc, Edinburgh, 126A, 1996, 363-374. Zbl0849.49014MR1386868
  13. [13] E. De Giorgi: Convergence problems for functionals and operators, in Proc. Int. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978, E. De Giorgi , E. Magenes, U. Mosco. ed., 131-188, Pitagora Editrice, Bologna, 1979. Zbl0405.49001MR533166
  14. [14] P. Marcellini: Some problems for functionals and operators, in Proc. Int. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978, E. De Giorgi, E. Magenes, U. Mosco. ed., 205-221, Pitagora Editrice, Bologna, 1979. Zbl0405.49021MR533168

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