Minimal rearrangements of Sobolev functions : a new proof
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 2, pp. 333-339. 
@article{AIHPC_2003__20_2_333_0,
     author = {Ferone, Adele and Volpicelli, Roberta},
     title = {Minimal rearrangements of {Sobolev} functions : a new proof},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {333--339},
     publisher = {Elsevier},
     volume = {20},
     number = {2},
     year = {2003},
     doi = {10.1016/S0294-1449(02)00012-4},
     mrnumber = {1961519},
     zbl = {1038.49039},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0294-1449(02)00012-4/}
}
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Ferone, Adele; Volpicelli, Roberta. Minimal rearrangements of Sobolev functions : a new proof. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 2, pp. 333-339. doi : 10.1016/S0294-1449(02)00012-4. http://www.numdam.org/articles/10.1016/S0294-1449(02)00012-4/

[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. | MR | Zbl

[2] Alvino A., Ferone V., Lions P.L., Trombetti G., Convex symmetrization and applications, Ann. Inst. H. Poincaré, Anal. Non Linéaire 14 (2) (1997) 275-293. | Numdam | MR | Zbl

[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. | MR | Zbl

[4] Aubin T., Problèmes isopérimétriques et espaces de Sobolev, C. R. Acad. Sci. Paris 280 (1975) 279-281. | MR | Zbl

[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. | MR | Zbl

[6] Brock F., Weighted Dirichlet-type inequalities for Steiner symmetrization, Calc. Var. Partial Differential Equations 8 (1999) 15-25. | MR | Zbl

[7] Brothers J.E., Ziemer W.P., Minimal rearrangements of Sobolev functions, J. Reine Angew. Math. 384 (1988) 153-179. | MR | Zbl

[8] Cianchi A., Pick L., Sobolev embeddings into BMO, VMO and L∞, Ark. Mat. 36 (2) (1998) 317-340. | Zbl

[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. | Zbl

[10] Duff G.F.D., A general integral inequality for the derivative of an equimeasurable rearrangement, Canad. J. Math. 28 (4) (1976) 793-804. | MR | Zbl

[11] Federer H., Geometric Measure Theory, Springer, Berlin, 1969. | MR | Zbl

[12] Fleming W., Rishel R., An integral formula for total gradient variation, Arch. Math. 11 (1960) 218-222. | MR | Zbl

[13] Friedman A., Mcleod R., Strict inequalities for integrals of decreasingly rearranged functions, Proc. Roy. Soc. Edinburgh 102-A (3-4) (1986) 277-289. | MR | Zbl

[14] Hilden K., Symmetrization of functions in Sobolev spaces and the isoperimetric inequality, Manuscripta Math. 18 (3) (1976) 215-235. | MR | Zbl

[15] Kawohl B., Rearrangements and Convexity of Level Sets in P.D.E., Lecture Notes in Math., 1150, Springer, Berlin, 1985. | MR | Zbl

[16] Klimov V.S., Imbedding theorems and geometric inequalities, Izv. Akad. Nauk USSR Ser. Mat. 40 (3) (1976) 645-671. | MR | Zbl

[17] Maz'Ja V.M., Sobolev Spaces, Springer, Berlin, 1985.

[18] Mossino J., Inégalités Isopérimétriques et Applications en Physic, Collection Travaux en Cours, Hermann Paris, 1984. | MR | Zbl

[19] Morrey C.B., Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. | MR | Zbl

[20] Pólya G., Szegö G., Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Studies, 27, Princeton University Press, Princeton, 1951. | MR | Zbl

[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. | MR | Zbl

[22] Ryff J.V., Measure preserving transformations and rearrangements, J. Math. Anal. Appl. 31 (3) (1970) 449-458. | MR | Zbl

[23] Sperner E., Zur Symmetrisierung von Funktionen auf Sphären, Math. Z. 134 (1973) 317-327. | MR | Zbl

[24] Sperner E., Symmetrisierung für Funktionen mehrerer reeler Variablen, Manuscripta Math. 11 (1974) 159-170. | MR | Zbl

[25] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. Cl. Sci. (4) 110 (1976) 353-372. | MR | Zbl

[26] Talenti G., A weighted version of a rearrangement inequality, Ann. Univ. Ferrara 43 (1997) 121-133. | MR | Zbl

[27] A. Uribe, Minima of Dirichlet norm and Topeliz operators, Preprint, 1985.

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