Sharp sobolev inequalities with lower order remainder terms

Transactions of the American Mathematical Society

Volumn 353, Issue 1, 2001, Pages 269-289

  Druet, Olivier ^a   Hebey, Emmanuel ^a   Vaugon, Michel ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044521322     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02698-2     Document Type: Article

References (26)

1. Aubin, T., Problèmes isopérimétriques et espaces de Sobolev, Journal of Differential Geometry, 11, 1976, 573-598. MR 56:6711
2. Aubin, T., Druet, O. and Hebey, E., Best constants in Sobolev inequalities for compact manifolds of nonpositive curvature, Comptes Rendus de l'Académie des Sciences, Paris, Sér. I Math. 326, 1998, 1117-1121. MR 99j:53042
3. Aubin, T. and Li, Y.Y., Sur la meilleure constante dans l'inégalité de Sobolev, Comptes Rendus de l'Académie des Sciences, Paris, Sér. I Math. 328, 1999, 135-138. MR 2000a:46048
4. Beckner, W., Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Annals of Mathematics, 138, 1993, 213-242. MR 94m:58232
5. Brezis, H. and Lieb, E.H., Sobolev inequalities with remainder terms, Journal of Functional Analysis, 62, 1985, 73-86. MR 86i:46033
6. Brezis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Communications on Pure and Applied Mathematics, 36, 1983, 437-477. MR 84h:35059
7. Caffarelli, L.A., Gidas, B. and Spruck, J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Communications on Pure and Applied Mathematics, 42, 1989, 271-297. MR 90c:35075
8. Croke, C.B., A sharp four dimensional isoperimetric inequality, Comment. Math. Helvetici, 59, 1984, 187-192. MR 85f:53060
9. Djadli, Z. and Druet, O., Extremal functions and Sobolev inequalities on compact manifolds, Preprint of the university of Cergy-Pontoise, Volume 13, April 1999.
10. Druet, O., Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds, Journal of Functional Analysis, 159, 1998, 217-242. MR 99m:53076
11. Druet, O., The best constants problem in Sobolev inequalities, Mathematische Annalen, 314, 1999, 327-346. MR 2000d:58033
12. Druet, O., Hebey, E. and Vaugon, M., Optimal Nash's inequalities on Riemannian manifolds: the influence of geometry, International Mathematics Research Notices, 1995, 735-779. CMP 99:16
13. Druet, O., Hebey, E. and Vaugon, M., Sharp Sobolev inequalities with lower order remainder terms, Preprint of the university of Cergy-Pontoise, Volume 3, January 1999.
14. Gilbarg, D. and Trudinger, N.S., Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, 224, Springer-Verlag, Second Edition, 1983. MR 86c:35035
15. Hebey, E., Sobolev spaces on Riemannian manifolds, Lecture Notes in Mathematics, 1635, Springer-Verlag, 1996. MR 98k:46049
16. Hebey, E., Fonctions extrémales pour une inégalité de Sobolev optimale dans la classe conforme de la sphère, Journal de Mathématiques Pures et Appliquées, 77, 1998, 721-733. MR 98j:58223
17. Hebey, E., Nonlinear analysis on manifolds: Sobolev spaces and inequalities, CIMS Lecture . Notes, Courant Institute of Mathematical Sciences, Volume 5, 1999. MR 2000e:58011
18. 2-Sobolev inequality after Djadli and Druet, Preprint, 1999.
19. Hebey, E. and Vaugon, M., Meilleures constantes dans le théorème d'inclusion de Sobolev, Annales de l'Institut Henri Poincaré, Analyse Non Linéaire, 13, 1996, 57-93. MR 96m:46054
20. Hebey, E. and Vaugon, M., The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Duke Mathematical Journal, 79, 1995, 235-279. MR 96c:53057
21. 2-Nash inequality, Preprint, 1999.
22. Kleiner, B., An isoperimetric comparison theorem, Inventiones Mathematicae, 108, 1992, 37-47. MR 92m:53056
23. Obata, M., The conjectures on conformai transformations of Riemannian manifolds, Journal of Differential Geometry, 6, 1971, 247-258. MR 46:2601
24. Talenti, G., Best constants in Sobolev inequality, Ann. di Matem. Pura ed Appl., 110, 1976, 353-372. MR 57:3846
25. Trudinger, N.S., Remarks concerning the conformai deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa, 22, 1968, 265-274. MR 39:2093
26. Weil, A., Sur les surfaces àcourbure négative, Comptes Rendus de l'Académie des Sciences de Paris, 182, 1926, 1069-1071.