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

Villani, Cédric; Cordero-Erausquin, Dario; Nazaret, Bruno

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

Pages

307-332

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