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.
Nguyen, H., Pinamonti, A., Squassina, M., Vecchi, E., New characterization of magnetic Sobolev spaces, <<ADVANCES IN NONLINEAR ANALYSIS>>, 2018; 7 (1): 227-245. [doi:10.1515/anona-2017-0239] [http://hdl.handle.net/10807/132126]
New characterization of magnetic Sobolev spaces
Squassina, Marco
Membro del Collaboration Group
;
2018
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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