@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/} }
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 SP - 333 EP - 339 VL - 20 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S0294-1449(02)00012-4/ DO - 10.1016/S0294-1449(02)00012-4 LA - en ID - AIHPC_2003__20_2_333_0 ER -
%0 Journal Article %A Ferone, Adele %A Volpicelli, Roberta %T Minimal rearrangements of Sobolev functions : a new proof %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 333-339 %V 20 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/S0294-1449(02)00012-4/ %R 10.1016/S0294-1449(02)00012-4 %G en %F AIHPC_2003__20_2_333_0
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] A remark on comparison result via Schwartz symmetrization, Proc. Roy. Soc. Edinburgh. 102-A (1-2) (1986) 37-48. | MR | Zbl
, , ,[2] Convex symmetrization and applications, Ann. Inst. H. Poincaré, Anal. Non Linéaire 14 (2) (1997) 275-293. | Numdam | MR | Zbl
, , , ,[3] 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] Problèmes isopérimétriques et espaces de Sobolev, C. R. Acad. Sci. Paris 280 (1975) 279-281. | MR | Zbl
,[5] A weighted isoperimetric inequality and applications to symmetrization, J. Inequal. Appl. 4 (3) (1999) 215-240. | MR | Zbl
, , , ,[6] Weighted Dirichlet-type inequalities for Steiner symmetrization, Calc. Var. Partial Differential Equations 8 (1999) 15-25. | MR | Zbl
,[7] Minimal rearrangements of Sobolev functions, J. Reine Angew. Math. 384 (1988) 153-179. | MR | Zbl
, ,[8] Sobolev embeddings into BMO, VMO and L∞, Ark. Mat. 36 (2) (1998) 317-340. | Zbl
, ,[9] 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] A general integral inequality for the derivative of an equimeasurable rearrangement, Canad. J. Math. 28 (4) (1976) 793-804. | MR | Zbl
,[11] Geometric Measure Theory, Springer, Berlin, 1969. | MR | Zbl
,[12] An integral formula for total gradient variation, Arch. Math. 11 (1960) 218-222. | MR | Zbl
, ,[13] Strict inequalities for integrals of decreasingly rearranged functions, Proc. Roy. Soc. Edinburgh 102-A (3-4) (1986) 277-289. | MR | Zbl
, ,[14] Symmetrization of functions in Sobolev spaces and the isoperimetric inequality, Manuscripta Math. 18 (3) (1976) 215-235. | MR | Zbl
,[15] Rearrangements and Convexity of Level Sets in P.D.E., Lecture Notes in Math., 1150, Springer, Berlin, 1985. | MR | Zbl
,[16] Imbedding theorems and geometric inequalities, Izv. Akad. Nauk USSR Ser. Mat. 40 (3) (1976) 645-671. | MR | Zbl
,[17] Sobolev Spaces, Springer, Berlin, 1985.
,[18] Inégalités Isopérimétriques et Applications en Physic, Collection Travaux en Cours, Hermann Paris, 1984. | MR | Zbl
,[19] Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. | MR | Zbl
,[20] Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Studies, 27, Princeton University Press, Princeton, 1951. | MR | Zbl
, ,[21] A co-area formula with applications to monotone rearrangement and to regularity, Arch. Rational Mech. Anal. 109 (3) (1990) 213-238. | MR | Zbl
, ,[22] Measure preserving transformations and rearrangements, J. Math. Anal. Appl. 31 (3) (1970) 449-458. | MR | Zbl
,[23] Zur Symmetrisierung von Funktionen auf Sphären, Math. Z. 134 (1973) 317-327. | MR | Zbl
,[24] Symmetrisierung für Funktionen mehrerer reeler Variablen, Manuscripta Math. 11 (1974) 159-170. | MR | Zbl
,[25] Best constant in Sobolev inequality, Ann. Mat. Pura Appl. Cl. Sci. (4) 110 (1976) 353-372. | MR | Zbl
,[26] 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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