Uniqueness of the polar factorisation and projection of a vector-valued mapping

G. R. Burton; R. J. Douglas

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 3, page 405-418
  • ISSN: 0294-1449

How to cite

top

Burton, G. R., and Douglas, R. J.. "Uniqueness of the polar factorisation and projection of a vector-valued mapping." Annales de l'I.H.P. Analyse non linéaire 20.3 (2003): 405-418. <http://eudml.org/doc/78585>.

@article{Burton2003,
author = {Burton, G. R., Douglas, R. J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {polar factorisation; monotone rearrangement; measure-preserving mappings; -projection},
language = {eng},
number = {3},
pages = {405-418},
publisher = {Elsevier},
title = {Uniqueness of the polar factorisation and projection of a vector-valued mapping},
url = {http://eudml.org/doc/78585},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Burton, G. R.
AU - Douglas, R. J.
TI - Uniqueness of the polar factorisation and projection of a vector-valued mapping
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 3
SP - 405
EP - 418
LA - eng
KW - polar factorisation; monotone rearrangement; measure-preserving mappings; -projection
UR - http://eudml.org/doc/78585
ER -

References

top
  1. [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. [2] Brenier Y., Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris Sér. I305 (1987) 805-808. Zbl0652.26017MR923203
  3. [3] Brenier Y., Polar factorisation and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math.44 (1991) 375-417. Zbl0738.46011MR1100809
  4. [4] Y. Brenier, A geometric presentation of the semi-geostrophic equations, Isaac Newton Institute report, 1996. 
  5. [5] Burton G.R., Douglas R.J., Rearrangements and polar factorisation of countably degenerate functions, Proc. Roy. Soc. Edinburgh128A (1998) 671-681. Zbl0910.28011MR1635400
  6. [6] Douglas R.J., Rearrangements of vector valued functions, with application to atmospheric and oceanic flows, SIAM J. Math. Anal.29 (1998) 891-902. Zbl0915.35025MR1617718
  7. [7] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. Zbl0322.90046MR463994
  8. [8] Larman D.G., On a conjecture of Klee and Martin for convex bodies, Proc. London Math. Soc. (3)23 (1971) 668-682. Zbl0245.52003MR293498
  9. [9] McCann R.J., Existence and uniqueness of monotone measure-preserving maps, Duke Math. J.80 (1995) 309-323. Zbl0873.28009MR1369395
  10. [10] Rockafellar R.T., Convex Analysis, Princeton University Press, Princeton, NJ, 1970. Zbl0193.18401MR274683
  11. [11] Royden H.L., Real Analysis, Macmillan, New York, 1988. Zbl0121.05501MR151555
  12. [12] Ryff J.V., Measure preserving transformations and rearrangements, J. Math. Anal. Appl.31 (1970) 449-458. Zbl0214.13701MR419734

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.