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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Sharp Sobolev inequalities with lower order remainder terms


Authors: Olivier Druet, Emmanuel Hebey and Michel Vaugon
Journal: Trans. Amer. Math. Soc. 353 (2001), 269-289
MSC (2000): Primary 58E35
DOI: https://doi.org/10.1090/S0002-9947-00-02698-2
Published electronically: September 15, 2000
MathSciNet review: 1783789
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Abstract: Given a smooth compact Riemannian $n$-manifold $(M,g)$, this paper deals with the sharp Sobolev inequality corresponding to the embedding of $H_1^2(M)$ in $L^{2n/(n-2)}(M)$ where the $L^2$ remainder term is replaced by a lower order term.


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Olivier Druet
Affiliation: Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
Email: Olivier.Druet@math.u-cergy.fr

Emmanuel Hebey
Affiliation: Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
Email: Emmanuel.Hebey@math.u-cergy.fr

Michel Vaugon
Affiliation: Université Pierre et Marie Curie, Département de Mathématiques, 4 place Jussieu, 75252 Paris cedex 05, France
Email: vaugon@math.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9947-00-02698-2
Received by editor(s): June 15, 1999
Published electronically: September 15, 2000
Article copyright: © Copyright 2000 American Mathematical Society