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Balls have the worst best Sobolev inequalities. Part II: variants and extensions

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Abstract

We continue our previous study of sharp Sobolev-type inequalities by means of optimal transport, started in (Maggi and Villani J. Geom. Anal. 15(1), 83–121 (2005)). In the present paper, we extend our results in various directions, including Gagliardo–Nirenberg, Faber–Krahn, logarithmic-Sobolev or Moser–Trudinger inequalities with trace terms. We also identify a class of domains for which there is no need for a trace term to cast the Sobolev inequality.

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Authors and Affiliations

  1. Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50141, Firenze, Italy

    F. Maggi

  2. UMPA, ENS Lyon, 46 allée d’Italie, 69364, Lyon Cedex 07, France

    C. Villani

Authors
  1. F. Maggi
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  2. C. Villani
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Correspondence to F. Maggi.

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Maggi, F., Villani, C. Balls have the worst best Sobolev inequalities. Part II: variants and extensions. Calc. Var. 31, 47–74 (2008). https://doi.org/10.1007/s00526-007-0105-x

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  • DOI: https://doi.org/10.1007/s00526-007-0105-x

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