SOBOLEV INEQUALITIES IN DISGUISE

Authors
BAKRY D COULHON T LEDOUX M SALOFFCOSTE L
Citation
D. Bakry et al., SOBOLEV INEQUALITIES IN DISGUISE, Indiana University mathematics journal, 44(4), 1995, pp. 1033-1074
Citations number
31
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Indiana University mathematics journal → ACNP
ISSN journal
00222518
Volume
44
Issue
4
Year of publication
1995
Pages
1033 - 1074
Database
ISI
SICI code
0022-2518(1995)44:4<1033:SIID>2.0.ZU;2-9
Abstract
We present a simple and direct proof of the equivalence of various fun ctional inequalities such as Sobolev or Nash inequalities. This proof applies in the context of Riemannian or sub-elliptic geometry, as well as on graphs and to certain non-local Sobolev norms. It only uses ele mentary cut-off arguments. This method has interesting consequences co ncerning Trudinger type inequalities.