no. 3
Uniqueness of the polar factorisation and projection of a vector-valued mapping
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 3, pp. 405-418. 
@article{AIHPC_2003__20_3_405_0,
     author = {Burton, G. R. and Douglas, R. J.},
     title = {Uniqueness of the polar factorisation and projection of a vector-valued mapping},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {405--418},
     publisher = {Elsevier},
     volume = {20},
     number = {3},
     year = {2003},
     doi = {10.1016/S0294-1449(02)00026-4},
     mrnumber = {1972869},
     zbl = {1038.28013},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0294-1449(02)00026-4/}
}
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Burton, G. R.; Douglas, R. J. Uniqueness of the polar factorisation and projection of a vector-valued mapping. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 3, pp. 405-418. doi : 10.1016/S0294-1449(02)00026-4. http://archive.numdam.org/articles/10.1016/S0294-1449(02)00026-4/

[1] J.-D. Benamou, Transformation conservant la mesure, mécanique des fluides incompressibles et modèle semi-géostrophique en météorologie, Thèse de 3ème cycle, Université de Paris IX-Dauphine, 1992.

[2] Brenier Y., Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris Sér. I 305 (1987) 805-808. | MR | Zbl

[3] Brenier Y., Polar factorisation and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math. 44 (1991) 375-417. | MR | Zbl

[4] Y. Brenier, A geometric presentation of the semi-geostrophic equations, Isaac Newton Institute report, 1996.

[5] Burton G.R., Douglas R.J., Rearrangements and polar factorisation of countably degenerate functions, Proc. Roy. Soc. Edinburgh 128A (1998) 671-681. | MR | Zbl

[6] Douglas R.J., Rearrangements of vector valued functions, with application to atmospheric and oceanic flows, SIAM J. Math. Anal. 29 (1998) 891-902. | MR | Zbl

[7] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. | MR | Zbl

[8] Larman D.G., On a conjecture of Klee and Martin for convex bodies, Proc. London Math. Soc. (3) 23 (1971) 668-682. | MR | Zbl

[9] Mccann R.J., Existence and uniqueness of monotone measure-preserving maps, Duke Math. J. 80 (1995) 309-323. | MR | Zbl

[10] Rockafellar R.T., Convex Analysis, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl

[11] Royden H.L., Real Analysis, Macmillan, New York, 1988. | MR | Zbl

[12] Ryff J.V., Measure preserving transformations and rearrangements, J. Math. Anal. Appl. 31 (1970) 449-458. | MR | Zbl

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