References
- Baernstein II , A . 1994 . “ A unified approach to symmetrization ” . In Partial Differential Equations of Ellyptic Type , Symposia Math. 35 Edited by: Alvino , A , Fabes , E and Talenti , G . Cambridge : Cambridge University Press . (Eds)
- Brothers , J and Ziemer , W . 1988 . Minimal rearrangements of Sobolev functions . Journal fur die Reine und Angewandte Mathematik , 384 : 153 – 179 .
- Hilden , K . 1976 . Symmetrization of functions in Sobolev spaces and the isoperimetric inequality . Manuscripta Mathematica , 18 : 215 – 235 .
- Kawohl , B . 1985 . “ Lecture Notes in Mathematics ” . In Rearrangements and convexity of level sets in PDE , Vol. 1150 , Berlin : Springer-Verlag .
- Sperner , E . 1974 . Symmetrisierung für Funktionen mehrerer reeller Variablen . Manuscripta Mathematica , 11 : 159 – 170 .
- Talenti , G . 1976 . Best constant in Sobolev inequality . Annali di Matematica Pura e Applicata , 110 : 353 – 372 .
- Burchard , A . 1997 . Steiner symmetrization is continuous in W 1 . Geometric and Functional Analysis , 7 : 823 – 860 .
- Cianchi , A and Fusco , N . 2002 . Functions of bounded variation and rearrangements . Archive for Rational Mechanics and Analysis , 165 : 1 – 40 .
- Cianchi , A and Fusco , N . 2003 . Steiner symmetric extremals in Pólya–Szegö type inequalities . Advances in Mathematics , (to appear)
- Esposito , L and Trombetti , C . 2004 . Convex symmetrization and Pólya–Szegö inequality . Nonlinear Analysis , 56 : 43 – 62 .
- Ferone , A and Volpicelli , R . 2003 . Minimal rearrangements of Sobolev functions: a new proof . Annales de l'Institut Henri Poincare. Analyse NonLinéaire , 20 : 333 – 339 .
- Ferone , A and Volpicelli , R . 2004 . Convex symmetrization: the equality case in the P′olya–Sze inequality . Calculus of Variations and Partial Differential Equations , 21 : 253 – 272 .
- Friedman , A and McLeod , B . 1986 . Strict inequalities for integrals of decreasingly rearranged functions . Proceedings of the Royal Society of Edinburgh , 102A : 277 – 289 .
- Kawohl , B . 1986 . On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems . Archive for Rational Mechanics and Analysis , 94 : 227 – 243 .
- Uribe , A . 1985 . Minima of the Dirichlet norm and Toeplitz operators . (Unpublished)
- Cianchi , A . 1996 . A sharp embedding theorem for Orlicz–Sobolev spaces . Indiana University Mathematics Journal , 45 : 39 – 65 .
- Cianchi , A . 1997 . Boundedness of solutions to variational problems under general growth conditions . Communications in Partial Differential Equations , 22 : 1629 – 1646 .
- Ambrosio , L , Fusco , N and Pallara , D . 2000 . Functions of Bounded Variation and Free Discontinuity Problems , Oxford : Oxford University Press .