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New characterizations of magnetic Sobolev spaces

Analysis of PDEs 2017-03-30 v1 Functional Analysis

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 L1L^1 appearing naturally in these contexts.

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Cite

@article{arxiv.1703.09801,
  title  = {New characterizations of magnetic Sobolev spaces},
  author = {Hoai-Minh Nguyen and Andrea Pinamonti and Marco Squassina and Eugenio Vecchi},
  journal= {arXiv preprint arXiv:1703.09801},
  year   = {2017}
}

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21 pages