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A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities

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Date
2004
Dewey
Probabilités et mathématiques appliquées
Sujet
Gagliardo–Nirenberg inequalities
Journal issue
Advances in Mathematics
Volume
182
Number
2
Publication date
03-2004
Article pages
307-332
DOI
http://dx.doi.org/10.1016/S0001-8708(03)00080-X
URI
https://basepub.dauphine.fr/handle/123456789/543
Collections
  • CEREMADE : Publications
Metadata
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Author
Villani, Cédric
Cordero-Erausquin, Dario
Nazaret, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
We show that mass transportation methods provide an elementary and powerful approach to the study of certain functional inequalities with a geometric content, like sharp Sobolev or Gagliardo-Nirenberg inequalities. The Euclidean structure of Rn plays no role in our approach: we establish these inequalities, together with cases of equality, for an arbitrary norm.

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