Calculus of Variations and Geometric Measure Theory
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H. M. Nguyen - A. Pinamonti - M. Squassina - E. Vecchi

New characterizations of magnetic Sobolev spaces

created by squassina on 26 Mar 2017

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Submitted Paper

Inserted: 26 mar 2017
Last Updated: 26 mar 2017

Pages: 21
Year: 2017

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 $L^1$ appearing naturally in these contexts.


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