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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Sharp Sobolev inequalities with lower order remainder terms
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by Olivier Druet, Emmanuel Hebey and Michel Vaugon PDF
Trans. Amer. Math. Soc. 353 (2001), 269-289 Request permission

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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Additional Information
  • 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
  • Received by editor(s): June 15, 1999
  • Published electronically: September 15, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 269-289
  • MSC (2000): Primary 58E35
  • DOI: https://doi.org/10.1090/S0002-9947-00-02698-2
  • MathSciNet review: 1783789