We establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in terms of nonlocal functionals. The first one is related to the BBM formula, due to Bourgain, Brezis and Mironescu. The second one is related to the work of the first author on the classical Sobolev spaces. We also study the convergence almost everywhere and the convergence in L1 appearing naturally in these contexts.

New characterizations of magnetic Sobolev spaces

Vecchi E.
2018

Abstract

We establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in terms of nonlocal functionals. The first one is related to the BBM formula, due to Bourgain, Brezis and Mironescu. The second one is related to the work of the first author on the classical Sobolev spaces. We also study the convergence almost everywhere and the convergence in L1 appearing naturally in these contexts.
Magnetic Sobolev spaces; new characterization; nonlocal functionals
File in questo prodotto:
File Dimensione Formato  
[Advances in Nonlinear Analysis] New characterizations of magnetic Sobolev spaces.pdf

accesso aperto

: Publisher’s version
Dimensione 867.81 kB
Formato Adobe PDF
867.81 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1125517
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 28
  • ???jsp.display-item.citation.isi??? 27
social impact