For a general open set, we characterize the compactness of the embedding for the homogeneous Sobolev space D1,p → Lq in 0 terms of the summability of its torsion function. In particular, for 1 ≤ q < p we obtain that the embedding is continuous if and only if it is compact. The proofs crucially exploit a torsional Hardy inequality that we investigate in detail.
Brasco L, Ruffini B (2017). Compact Sobolev embeddings and torsion functions. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 34(4), 817-843 [10.1016/j.anihpc.2016.05.005].
Compact Sobolev embeddings and torsion functions
Ruffini B
2017
Abstract
For a general open set, we characterize the compactness of the embedding for the homogeneous Sobolev space D1,p → Lq in 0 terms of the summability of its torsion function. In particular, for 1 ≤ q < p we obtain that the embedding is continuous if and only if it is compact. The proofs crucially exploit a torsional Hardy inequality that we investigate in detail.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
braruf.pdf
accesso aperto
Tipo:
Postprint / Author's Accepted Manuscript (AAM) - versione accettata per la pubblicazione dopo la peer-review
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
1.08 MB
Formato
Adobe PDF
|
1.08 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
