Calculus of Variations and Geometric Measure Theory
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F. Maggi - C. Villani

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

created by maggi on 20 Apr 2006
modified on 14 Mar 2007


Accepted Paper

Inserted: 20 apr 2006
Last Updated: 14 mar 2007

Journal: Calc. Var. Partial Differential Equations
Year: 2007


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.


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