A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities
Nazaret, Bruno ; Cordero-Erausquin, Dario ; Villani, Cédric
HAL, hal-00157943 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  46E35, 39B72,  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 
@article{hal-00157943,
     author = {Nazaret, Bruno and Cordero-Erausquin, Dario and Villani, C\'edric},
     title = {A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00157943}
}

Nazaret, Bruno; Cordero-Erausquin, Dario; Villani, Cédric. A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00157943/