Citation
T. Aubin et Yy. Li, On the best Sobolev inequality, J MATH P A, 78(4), 1999, pp. 353-387
Citations number
37
Categorie Soggetti
Mathematics
Journal title
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
ISSN journal
00217824
→ ACNP
Volume
78
Issue
4
Year of publication
1999
Pages
353 - 387
Database
ISI
SICI code
0021-7824(199904)78:4<353:OTBSI>2.0.ZU;2-8
Abstract
We prove that the best constant in the Sobolev inequality (W-1,W-p subset o
f L-p* with 1/p* = 1/p - 1/n and 1 < p < n) is achieved on compact Riemanni
an manifolds, or only complete under some hypotheses. We also establish str
onger inequalities where the norms are to some exponent which seems optimal
. (C) Elsevier, Paris.