Answering a question raised by Y.X. Huang, we prove what follows: if O is a bounded smooth domain and p > 1, then the mapping q → λq |O|^(p/q) is decreasing in ]0, p*[ and Lipschitz continuous on compact subsets of ]0, p*[, λq being the p-th power of the best Sobolev constant for the embedding of W^(1,p)(O) into L^q(O)
On a problem of Huang concerning best constants in Sobolev embeddings
IANNIZZOTTO, ANTONIO
2015-01-01
Abstract
Answering a question raised by Y.X. Huang, we prove what follows: if O is a bounded smooth domain and p > 1, then the mapping q → λq |O|^(p/q) is decreasing in ]0, p*[ and Lipschitz continuous on compact subsets of ]0, p*[, λq being the p-th power of the best Sobolev constant for the embedding of W^(1,p)(O) into L^q(O)
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Anello-Faraci-Iannizzotto-AMAP.pdf
Solo gestori archivio
Descrizione: Articolo principale
Tipologia:
versione editoriale (VoR)
Dimensione
440.51 kB
Formato
Adobe PDF
|
440.51 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
