Minimal rearrangements of Sobolev functions : a new proof

Adele Ferone; Roberta Volpicelli

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

  • Volume: 20, Issue: 2, page 333-339
  • ISSN: 0294-1449

How to cite

top

Ferone, Adele, and Volpicelli, Roberta. "Minimal rearrangements of Sobolev functions : a new proof." Annales de l'I.H.P. Analyse non linéaire 20.2 (2003): 333-339. <http://eudml.org/doc/78581>.

@article{Ferone2003,
author = {Ferone, Adele, Volpicelli, Roberta},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {polar factorization; rearrangements; Pólya-Szegő type inequalities},
language = {eng},
number = {2},
pages = {333-339},
publisher = {Elsevier},
title = {Minimal rearrangements of Sobolev functions : a new proof},
url = {http://eudml.org/doc/78581},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Ferone, Adele
AU - Volpicelli, Roberta
TI - Minimal rearrangements of Sobolev functions : a new proof
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 2
SP - 333
EP - 339
LA - eng
KW - polar factorization; rearrangements; Pólya-Szegő type inequalities
UR - http://eudml.org/doc/78581
ER -

References

top
  1. [1] Alvino A., Lions P.L., Trombetti G., A remark on comparison result via Schwartz symmetrization, Proc. Roy. Soc. Edinburgh.102-A (1–2) (1986) 37-48. Zbl0597.35005MR837159
  2. [2] Alvino A., Ferone V., Lions P.L., Trombetti G., Convex symmetrization and applications, Ann. Inst. H. Poincaré, Anal. Non Linéaire14 (2) (1997) 275-293. Zbl0877.35040MR1441395
  3. [3] Aronsson G., Talenti G., Estimating the integral of a function in terms of a distribution function of its gradient, Boll. Un. Mat. Ital. (5)18-B (3) (1981) 885-894. Zbl0476.49030MR641744
  4. [4] Aubin T., Problèmes isopérimétriques et espaces de Sobolev, C. R. Acad. Sci. Paris280 (1975) 279-281. Zbl0295.53024MR407905
  5. [5] Betta M.F., Brock F., Mercaldo A., Posteraro M.R., A weighted isoperimetric inequality and applications to symmetrization, J. Inequal. Appl.4 (3) (1999) 215-240. Zbl1029.26018MR1734159
  6. [6] Brock F., Weighted Dirichlet-type inequalities for Steiner symmetrization, Calc. Var. Partial Differential Equations8 (1999) 15-25. Zbl0947.35056MR1666874
  7. [7] Brothers J.E., Ziemer W.P., Minimal rearrangements of Sobolev functions, J. Reine Angew. Math.384 (1988) 153-179. Zbl0633.46030MR929981
  8. [8] Cianchi A., Pick L., Sobolev embeddings into BMO, VMO and L∞, Ark. Mat.36 (2) (1998) 317-340. Zbl1035.46502
  9. [9] De Giorgi E., Su una teoria generale della misura (r−1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl.36 (4) (1954) 191-213. Zbl0055.28504
  10. [10] Duff G.F.D., A general integral inequality for the derivative of an equimeasurable rearrangement, Canad. J. Math.28 (4) (1976) 793-804. Zbl0342.26015MR409745
  11. [11] Federer H., Geometric Measure Theory, Springer, Berlin, 1969. Zbl0874.49001MR257325
  12. [12] Fleming W., Rishel R., An integral formula for total gradient variation, Arch. Math.11 (1960) 218-222. Zbl0094.26301MR114892
  13. [13] Friedman A., McLeod R., Strict inequalities for integrals of decreasingly rearranged functions, Proc. Roy. Soc. Edinburgh102-A (3–4) (1986) 277-289. Zbl0601.49012MR852361
  14. [14] Hilden K., Symmetrization of functions in Sobolev spaces and the isoperimetric inequality, Manuscripta Math.18 (3) (1976) 215-235. Zbl0365.46031MR409773
  15. [15] Kawohl B., Rearrangements and Convexity of Level Sets in P.D.E., Lecture Notes in Math., 1150, Springer, Berlin, 1985. Zbl0593.35002MR810619
  16. [16] Klimov V.S., Imbedding theorems and geometric inequalities, Izv. Akad. Nauk USSR Ser. Mat.40 (3) (1976) 645-671. Zbl0332.46022MR420250
  17. [17] Maz'ja V.M., Sobolev Spaces, Springer, Berlin, 1985. Zbl0727.46017
  18. [18] Mossino J., Inégalités Isopérimétriques et Applications en Physic, Collection Travaux en Cours, Hermann Paris, 1984. Zbl0537.35002MR733257
  19. [19] Morrey C.B., Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. Zbl0142.38701MR202511
  20. [20] Pólya G., Szegö G., Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Studies, 27, Princeton University Press, Princeton, 1951. Zbl0044.38301MR43486
  21. [21] Rakotoson J.M., Temam R., A co-area formula with applications to monotone rearrangement and to regularity, Arch. Rational Mech. Anal.109 (3) (1990) 213-238. Zbl0735.49039MR1025171
  22. [22] Ryff J.V., Measure preserving transformations and rearrangements, J. Math. Anal. Appl.31 (3) (1970) 449-458. Zbl0214.13701MR419734
  23. [23] Sperner E., Zur Symmetrisierung von Funktionen auf Sphären, Math. Z.134 (1973) 317-327. Zbl0283.26015MR340558
  24. [24] Sperner E., Symmetrisierung für Funktionen mehrerer reeler Variablen, Manuscripta Math.11 (1974) 159-170. Zbl0268.26011MR328000
  25. [25] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. Cl. Sci. (4)110 (1976) 353-372. Zbl0353.46018MR463908
  26. [26] Talenti G., A weighted version of a rearrangement inequality, Ann. Univ. Ferrara43 (1997) 121-133. Zbl0936.26007MR1686750
  27. [27] A. Uribe, Minima of Dirichlet norm and Topeliz operators, Preprint, 1985. 

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.