Calculus of Variations and Partial Differential Equations

, Volume 31, Issue 1, pp 47–74

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

Original Article

DOI: 10.1007/s00526-007-0105-x

Cite this article as:
Maggi, F. & Villani, C. Calc. Var. (2008) 31: 47. doi:10.1007/s00526-007-0105-x

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.

PACS

26D1535R4546E35

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