Minimal rearrangements, strict convexity and critical points

International Journal of Phytoremediation

Volumn 85, Issue 1-3, 2006, Pages 67-85

  Cianchi, Andrea ^a   Fusco, Nicola ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

46E30; Asymmetry estimates; Dirichlet integrals; Isoperimetric inequalities; Mathematics Subject Classifications: 46E35; Sobolev spaces; Symmetrization

Indexed keywords

EID: 85065359909     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810500277777     Document Type: Article

References (18)

1. 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)
2. Brothers, J, and Ziemer, W. 1988. Minimal rearrangements of Sobolev functions. Journal fur die Reine und Angewandte Mathematik, 384: 153-179.
3. Hilden, K. 1976. Symmetrization of functions in Sobolev spaces and the isoperimetric inequality. Manuscripta Mathematica, 18: 215-235.
4. Kawohl, B. 1985. “ Lecture Notes in Mathematics ”. In Rearrangements and convexity of level sets in PDE, Vol. 1150, Berlin: Springer-Verlag.
5. Sperner, E. 1974. Symmetrisierung für Funktionen mehrerer reeller Variablen. Manuscripta Mathematica, 11: 159-170.
6. Talenti, G. 1976. Best constant in Sobolev inequality. Annali di Matematica Pura e Applicata, 110: 353-372.
7. 1 . Geometric and Functional Analysis, 7: 823-860.
8. Cianchi, A, and Fusco, N. 2002. Functions of bounded variation and rearrangements. Archive for Rational Mechanics and Analysis, 165: 1-40.
9. Cianchi, A, and Fusco, N. 2003. Steiner symmetric extremals in Pólya-Szegö type inequalities. Advances in Mathematics, (to appear)
10. Esposito, L, and Trombetti, C. 2004. Convex symmetrization and Pólya-Szegö inequality. Nonlinear Analysis, 56: 43-62.
11. 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.
12. 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.
13. Friedman, A, and McLeod, B. 1986. Strict inequalities for integrals of decreasingly rearranged functions. Proceedings of the Royal Society of Edinburgh, 102A: 277-289.
14. 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.
15. Uribe, A. 1985. Minima of the Dirichlet norm and Toeplitz operators. (Unpublished)
16. Cianchi, A. 1996. A sharp embedding theorem for Orlicz-Sobolev spaces. Indiana University Mathematics Journal, 45: 39-65.
17. Cianchi, A. 1997. Boundedness of solutions to variational problems under general growth conditions. Communications in Partial Differential Equations, 22: 1629-1646.
18. Ambrosio, L, Fusco, N, and Pallara, D. 2000. Functions of Bounded Variation and Free Discontinuity Problems, Oxford: Oxford University Press.