New characterizations of magnetic Sobolev spaces - Nguyen Hoai-Minh; Pinamonti Andrea; Squassina Marco; Vecchi Eugenio (Advances in Nonlinear Analysis, 2018)
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{L^{1}} appearing naturally in these contexts.