New characterizations of magnetic Sobolev spaces
type: Item
instance of: scholarly article
title: New characterizations of magnetic Sobolev spaces
zbMATH Open document ID: 1429.49007
author: Hoai-Minh Nguyen
author: Andrea Pinamonti
author: Marco Squassina
author: Eugenio Vecchi
published in: Advances in Nonlinear Analysis
publication date: 2018-05-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1703.09801
review text: This paper deals with characterization of magnetic Sobolev spaces. Actually, using nonlocal functionals, the authors establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in the whole space setting. These characterizations are related to the Bourgain, Brezis and Mironescu formula and to the work of the first author on Sobolev space. The convergence almost everywhere and the \(L^1\) convergence are also studied.
reviewed by: Gisèle M. Mophou
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 82D99
zbMATH DE Number: 6867309
zbMATH Keywords: magnetic Sobolev spaces
zbMATH Keywords: new characterization
zbMATH Keywords: nonlocal functionals
MaRDI profile type: Publication
OpenAlex ID: W2610841850
arXiv ID: 1703.09801
cites work: A semilinear Schrödinger equation in the presence of a magnetic field
cites work: Schrödinger operators with magnetic fields. I: General interactions
cites work: Q3159214
cites work: Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
cites work: A new characterization of Sobolev spaces
cites work: New approximations of the total variation and filters in imaging
cites work: The BBM formula revisited
cites work: Two subtle convex nonlocal approximations of the BV-norm
cites work: Ground states for fractional magnetic operators
cites work: On an open question about functions of bounded variation.
cites work: Q3480488
cites work: Magnetic Relativistic Schrödinger Operators and Imaginary-time Path Integrals
cites work: Q3249645
cites work: Analysis.
cites work: Q3838069
cites work: Some new characterizations of Sobolev spaces
cites work: Further characterizations of Sobolev spaces
cites work: \(\Gamma\)-convergence, Sobolev norms, and BV functions
cites work: Some inequalities related to Sobolev norms
cites work: Estimates for the topological degree and related topics
cites work: Magnetic BV-functions and the Bourgain-Brezis-Mironescu formula
cites work: The Maz'ya-Shaposhnikova limit in the magnetic setting
cites work: A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
cites work: On formulae decoupling the total variation of BV~functions
cites work: Q3909512
cites work: Bourgain-Brézis-Mironescu formula for magnetic operators
cites work: Q5607484
DOI: 10.1515/ANONA-2017-0239
description: scientific article