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

Villani, Cédric; Cordero-Erausquin, Dario; Nazaret, Bruno (2004), A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities, Advances in Mathematics, 182, 2, p. 307-332. http://dx.doi.org/10.1016/S0001-8708(03)00080-X

Type
Article accepté pour publication ou publié
Date
2004
Journal name
Advances in Mathematics
Volume
182
Number
2
Pages
307-332
Publication identifier
http://dx.doi.org/10.1016/S0001-8708(03)00080-X
Metadata
Show full item record
Author(s)
Villani, Cédric
Cordero-Erausquin, Dario
Nazaret, Bruno
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.
Subjects / Keywords
Gagliardo–Nirenberg inequalities

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