Rearrangements and polar factorisation of countably degenerate functions

Royal Society of Edinburgh - Proceedings A

Volumn 128, Issue 4, 1998, Pages 671-681

  Burton, G R ^a   Douglas, R J ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22044456113     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500021703     Document Type: Article

References (10)

1. Y. Brenier. Polar factorisation and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44 (1991), 375-417.
2. R. J. Douglas. Rearrangements of vector valued functions, with application to atmospheric and oceanic flows. SIAM J. Math. Anal. 29 (1998), 891-902.
3. W. Gangbo. An elementary proof of the polar factorization of vector-valued functions. Arch. Rational Mech. Anal. 128 (1994), 381-99.
4. W. Gangbo and R. J. McCann. The geometry of optimal transportation. Acta Math. 177 (1996), 113-61.
5. P. R. Halmos. Measure Theory (New York: Van Nostrand, 1950).
6. G. H. Hardy, J. E. Littlewood and G. Pólya. Inequalities (Cambridge: Cambridge University Press, 1934).
7. A. S. Kechris. Classical Descriptive Set Theory (New York: Springer, 1995).
8. R. J. McCann. Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80 (1995), 309-23.
9. R. T. Rockafellar. Convex Analysis (Princeton, NJ: Princeton University Press, 1970).
10. J. V. Ryff. Measure preserving transformations and rearrangements. J. Math. Anal. Appl. 31 (1970), 449-58.