New characterizations of magnetic Sobolev spaces
This paper deals with characterization of magnetic Sobolev spaces. Actually, using nonlocal functionals, the authors establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in the whole space setting. These characterizations are related to the Bourgain, Brezis and Mironescu formula and to the work of the first author on Sobolev space. The convergence almost everywhere and the \(L^1\) convergence are also studied.
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