Prescribing the jacobian determinant in Sobolev spaces

Dong Ye

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 3, page 275-296
  • ISSN: 0294-1449

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Ye, Dong. "Prescribing the jacobian determinant in Sobolev spaces." Annales de l'I.H.P. Analyse non linéaire 11.3 (1994): 275-296. <http://eudml.org/doc/78332>.

@article{Ye1994,
author = {Ye, Dong},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {existence; nonexistence; Jacobian determinant},
language = {eng},
number = {3},
pages = {275-296},
publisher = {Gauthier-Villars},
title = {Prescribing the jacobian determinant in Sobolev spaces},
url = {http://eudml.org/doc/78332},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Ye, Dong
TI - Prescribing the jacobian determinant in Sobolev spaces
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 3
SP - 275
EP - 296
LA - eng
KW - existence; nonexistence; Jacobian determinant
UR - http://eudml.org/doc/78332
ER -

References

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  1. [1] J. Moser, On the Volume Elements on a Manifold, Trans. Amer. Math. Soc., Vol. 120, 1965, pp. 286-294. Zbl0141.19407MR182927
  2. [2] B. Dacorogna and J. Moser, On a Partial Differential Equation Involving the Jacobian Determinant, Ann. I.H.P. Analyse Non Linéaire, Vol. 7, 1990, pp. 1-26. Zbl0707.35041MR1046081
  3. [3] R.A. Adams, Sobolev Spaces, Academic Press, 1975. Zbl0314.46030MR450957
  4. [4] J.M. Ball, Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rational Mech. Anal., No. 63, 1977, pp. 337-403. Zbl0368.73040MR475169
  5. [5] J.M. Ball, Global Invertibility of Sobolev Functions and the Interpenetration of Matter, Proceeding of the Royal Society of Edinburgh, 88A, 1987, pp. 315-328. Zbl0478.46032MR616782
  6. [6] P. Bauman, N.C. Owen and D. Phillips, Maximum Principles and a priori Estimates for an Incompressible Material in Nonlinear Elasticity, preprint. Zbl0777.35014MR1179283
  7. [7] J.-P. Bourguignon and H. Brezis, Remarks on the Euler Equation, Journal of Function Analysis, 15, 1974, pp. 341-363. Zbl0279.58005MR344713
  8. [8] R.R. Coifman, P.L. Lions, Y. Meyer and S. Semmes, Compacité par compensation et Espace de Hardy, C. R. Acad. Sci. Paris, 309, Série I, 1989, pp. 945-949. Zbl0684.46044
  9. [9] G. Geymonat and P. Grisvard, Problèmes aux limites elliptiques dans Lp, Publications Math. Orsay, 1964. 
  10. [10] F. Hélein, Private Communication, 1992. 
  11. [11] J.L. Lions, Problèmes aux limites dans les equations aux dérivées partielles, Séminaire de Math. Sup., Université de Montréal, 1962. Zbl0143.14003MR251372
  12. [12] P. Le Tallec and J.T. Oden, Existence and Characterization of Hydrostatic Pressure in Finite Deformations of Incompressible Elastic Bodies, J. Elasticity, No. 11, 1981, pp. 341-358. Zbl0483.73035MR637620
  13. [13] J. Milnor, Remarks on Infinite Dimensional Lie Groups, Relativité, Groupes et Topologie II, Les Houches, Session XL, B. S. DEWITT and P. STORA Eds., 1983, pp. 1007- 1057. Zbl0594.22009MR830252
  14. [14] S. Müller, Det = det. A Remark on the Distributional Determinant, C. R. Acad. Sci. Paris, 311, Série I, 1990, pp. 13-17. Zbl0717.46033MR1062920
  15. [15] A.I. Shnirel'man, On the Geometry of the Group of Diffeomorphisms and the Dynamics of an Ideal Incompressible Fluid, Math. USSR Sbornik, Vol. 56, No. 1, 1987, pp. 79-105. Zbl0725.58005
  16. [16] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. Zbl0207.13501MR290095

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