no. 3
Prescribing the jacobian determinant in Sobolev spaces
Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) no. 3, pp. 275-296. 
@article{AIHPC_1994__11_3_275_0,
     author = {Ye, Dong},
     title = {Prescribing the jacobian determinant in {Sobolev} spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {275--296},
     publisher = {Gauthier-Villars},
     volume = {11},
     number = {3},
     year = {1994},
     mrnumber = {1277896},
     zbl = {0834.35047},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1994__11_3_275_0/}
}
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
SP  - 275
EP  - 296
VL  - 11
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1994__11_3_275_0/
LA  - en
ID  - AIHPC_1994__11_3_275_0
ER  - 
%0 Journal Article
%A Ye, Dong
%T Prescribing the jacobian determinant in Sobolev spaces
%J Annales de l'I.H.P. Analyse non linéaire
%D 1994
%P 275-296
%V 11
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1994__11_3_275_0/
%G en
%F AIHPC_1994__11_3_275_0
Ye, Dong. Prescribing the jacobian determinant in Sobolev spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) no. 3, pp. 275-296. http://www.numdam.org/item/AIHPC_1994__11_3_275_0/

[1] J. Moser, On the Volume Elements on a Manifold, Trans. Amer. Math. Soc., Vol. 120, 1965, pp. 286-294. | MR | Zbl

[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. | Numdam | MR | Zbl

[3] R.A. Adams, Sobolev Spaces, Academic Press, 1975. | MR | Zbl

[4] J.M. Ball, Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rational Mech. Anal., No. 63, 1977, pp. 337-403. | MR | Zbl

[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. | MR | Zbl

[6] P. Bauman, N.C. Owen and D. Phillips, Maximum Principles and a priori Estimates for an Incompressible Material in Nonlinear Elasticity, preprint. | MR

[7] J.-P. Bourguignon and H. Brezis, Remarks on the Euler Equation, Journal of Function Analysis, 15, 1974, pp. 341-363. | MR | Zbl

[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. | Zbl

[9] G. Geymonat and P. Grisvard, Problèmes aux limites elliptiques dans Lp, Publications Math. Orsay, 1964.

[10] F. Hélein, Private Communication, 1992.

[11] J.L. Lions, Problèmes aux limites dans les equations aux dérivées partielles, Séminaire de Math. Sup., Université de Montréal, 1962. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[14] S. Müller, Det = det. A Remark on the Distributional Determinant, C. R. Acad. Sci. Paris, 311, Série I, 1990, pp. 13-17. | MR | Zbl

[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. | Zbl

[16] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. | MR | Zbl