Magnetic BV-functions and the Bourgain–Brezis–Mironescu formula-Reference-Cited by-同舟云学术

Magnetic BV-functions and the Bourgain–Brezis–Mironescu formula

Published:2019-07-01 Issue:3 Volume:12 Page:225-252
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:
Short-container-title:

Author:

Pinamonti Andrea¹,Squassina Marco²,Vecchi Eugenio³

Affiliation:

1. Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38123Povo (TN), Italy

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

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

Abstract

AbstractWe prove a general magnetic Bourgain–Brezis–Mironescu formula which extends the one obtained in [37] in the Hilbert case setting. In particular, after developing a rather complete theory of magnetic bounded variation functions, we prove the validity of the formula in this class.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2017-0019/pdf

Reference76 articles.

1. BV functions and traces;Rend. Semin. Mat. Univ. Padova,1978

2. Anisotropic fractional perimeters;J. Differential Geom.,2014

3. The Maz’ya–Shaposhnikova limit in the magnetic setting;J. Math. Anal. Appl.,2017

4. Some new characterizations of Sobolev spaces;J. Funct. Anal.,2006

Cited by 35 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Magnetic fractional Poincaré inequality in punctured domains;Journal of Mathematical Analysis and Applications;2024-07

2. Asymptotically linear magnetic fractional problems;Applied Mathematics Letters;2024-05

3. A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces;Nonlinear Analysis;2024-04

4. Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains;Calculus of Variations and Partial Differential Equations;2024-01-09

5. On a class of fractional Kirchhoff–Schrödinger–Poisson systems involving magnetic fields;Communications in Nonlinear Science and Numerical Simulation;2023-09