New characterization of magnetic Sobolev spaces

Marco Squassina

doi:10.1515/anona-2017-0239

New characterization of magnetic Sobolev spaces

Marco Squassina^*

^*Corresponding author

Research output: Contribution to journal › Article

23 Citations (Scopus)

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 L 1 appearing naturally in these contexts.

Original language	English
Pages (from-to)	227-245
Number of pages	19
Journal	Advances in Nonlinear Analysis
Volume	7
DOIs	https://doi.org/10.1515/anona-2017-0239
Publication status	Published - 2018

Keywords

Magnetic Sobolev spaces

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10.1515/anona-2017-0239

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title = "New characterization of magnetic Sobolev spaces",

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 L 1 appearing naturally in these contexts.",

keywords = "Magnetic Sobolev spaces, Magnetic Sobolev spaces",

author = "Marco Squassina",

year = "2018",

doi = "10.1515/anona-2017-0239",

language = "English",

volume = "7",

pages = "227--245",

journal = "Advances in Nonlinear Analysis",

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TY - JOUR

T1 - New characterization of magnetic Sobolev spaces

AU - Squassina, Marco

PY - 2018

Y1 - 2018

N2 - 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 L 1 appearing naturally in these contexts.

AB - 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 L 1 appearing naturally in these contexts.

KW - Magnetic Sobolev spaces

UR - http://hdl.handle.net/10807/132126

U2 - 10.1515/anona-2017-0239

DO - 10.1515/anona-2017-0239

M3 - Article

SN - 2191-9496

VL - 7

SP - 227

EP - 245

JO - Advances in Nonlinear Analysis

JF - Advances in Nonlinear Analysis

ER -

New characterization of magnetic Sobolev spaces

Abstract

Keywords

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