Best constants in second-order Sobolev inequalities on compact Riemannian manifolds in the presence of symmetries

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Let (M,g) be a smooth compact 3\leq n-dimensional Riemannian manifold, and G a subgroup of the isometry group of (M,g). We establish the best constants in second-order for a Sobolev inequality when the functions are G-invariant.

Anahtar Kelimeler:

Best constants, compact Riemannian manifolds, Sobolev inequalities, isometries

Best constants in second-order Sobolev inequalities on compact Riemannian manifolds in the presence of symmetries

Keywords:

Best constants, compact Riemannian manifolds, Sobolev inequalities, isometries,

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Aubin, T.: Espaces de Sobolev sur les variétés Riemanniennes. Bull. Sc. Math. 100, 149—173 (1976).
Aubin, T.: Problemes isopérimétriques et espaces de Sobolev. J. Differ. Geom. 11, 573—598 (1976).
Biezuner, R., Montenegro, M.: Best constants in second—order Sobolev inequalities on Riemannian manifolds and applications. J. Math. Pures Appl. 82, 457—502 (2003).
Cherrier, P.: Meilleures constantes dans des inégalités relatives aux espaces de Sobolev. Bull. Sci. Math. 108, 225—262 (1984).
Djadli, Z., Hebey, E., Ledoux, M.: Paneitz—type operators and applications. Duke Math. J. 104, 12%169 (2000).
Druet, 0.: The best constants problem in Sobolev inequalities. Math. Ann. 314, 327—346 (1999).
Lieb, E.: Sharp constants in the Hardy—Littlewood—Sobolev and related inqualities. Ann Math. 118, 34%374 (1983).
Talenti, G.: Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 3, 697—718 (1976).
Mohammed ALI Received: 09.07.2009
Department of Mathematics and Statistics,
Jordan University of Science and Technology,
Irbid, 22110, JORDAN
e—mail: myali@just.edu.jo