Inserted: 20 apr 2006
Last Updated: 14 mar 2007
Journal: Calc. Var. Partial Differential Equations
We continue our previous study of sharp Sobolev-type inequalities by means of optimal transport, started in Part I. 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.