New characterizations of magnetic Sobolev spaces-Reference-Cited by-同舟云学术

New characterizations of magnetic Sobolev spaces

Published:2018-05-01 Issue:2 Volume:7 Page:227-245
ISSN:2191-9496
Container-title:Advances in Nonlinear Analysis
language:
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Author:

Nguyen Hoai-Minh¹,Pinamonti Andrea²,Squassina Marco³,Vecchi Eugenio⁴

Affiliation:

1. Department of Mathematics, Ecole Polytechnique Federale de Lausanne, EPFL SB CAMA, Station 8, CH-1015Lausanne, Switzerland

2. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123Povo (Trento), Italy

3. Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121Brescia, Italy

4. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126Bologna, Italy

Abstract

AbstractWe 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.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/downloadpdf/journals/anona/7/2/article-p227.xml

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