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

Original Article


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.


26D15 35R45 46E35 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly
  2. 2.UMPA, ENS LyonLyon Cedex 07France

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