In this note we prove the following theorem in any Carnot group of step two G: lim s↗1/2 (1 − 2s)PH,s(E) = 4 √_ PH(E). Here, PH(E) represents the horizontal perimeter of a measurable set E ⊂ G, whereas the nonlocal horizontal perimeter PH,s(E) is a heat based Besov seminorm. This result represents a dimensionless sub-Riemannian counterpart of a famous characterisation of Bourgain-Brezis-Mironescu and Davila.
A Bourgain–Brezis–Mironescu–Dávila theorem in Carnot groups of step two
Tralli, GiulioUltimo
2023
Abstract
In this note we prove the following theorem in any Carnot group of step two G: lim s↗1/2 (1 − 2s)PH,s(E) = 4 √_ PH(E). Here, PH(E) represents the horizontal perimeter of a measurable set E ⊂ G, whereas the nonlocal horizontal perimeter PH,s(E) is a heat based Besov seminorm. This result represents a dimensionless sub-Riemannian counterpart of a famous characterisation of Bourgain-Brezis-Mironescu and Davila.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
CAG-2023-0031-0002-a003.pdf
solo gestori archivio
Descrizione: versione editoriale
Tipologia:
Full text (versione editoriale)
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
241.63 kB
Formato
Adobe PDF
|
241.63 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
|
2004.08529.pdf
solo gestori archivio
Descrizione: Pre-print
Tipologia:
Pre-print
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
238.57 kB
Formato
Adobe PDF
|
238.57 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
