Extremal functions for an optimal Sobolev inequality in the conformal class of the sphere

DOI10.1016/S0021-7824(98)80006-8zbMath0914.53026OpenAlexW1972955518MaRDI QIDQ1267284

Emmanuel Hebey

Publication date: 24 June 1999

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-7824(98)80006-8

zbMATH Keywords

Sobolev inequalitiesbest constantsYamabe functional

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Cites Work

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• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Sobolev spaces on Riemannian manifolds
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• Best constants in the Sobolev imbedding theorem
• The conjectures on conformal transformations of Riemannian manifolds
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents