New characterizations of magnetic Sobolev spaces

2017/03/26 by Hoài-Minh Nguyên, Nguyen, Hoai-Minh, Andrea Pinamonti +5 · 1 citation
Mathematics · #26A33 #49A50 #82D99 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.09801

openalex publication_date 2017/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Characterizations of the Sobolev norms and the total variation via nonlocal functionals, and related problems

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