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Inequalities involving Aharonov-Bohm magnetic potentials in dimensions 2 and 3

par Bonheure, Denis ;Dolbeault, Jean;Esteban, María José;Laptev, Ari;Loss, Michael
Référence Reviews in mathematical physics, 33, 3, 2150006, 29 pp.
Publication Publié, 2021-01-01

Article révisé par les pairs

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Résumé :

This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schrödinger operators involving Aharonov-Bohm magnetic potentials, and to some consequences. As symmetry plays an important role for establishing optimality results, we shall consider various cases corresponding to a circle, a two-dimensional sphere or a two-dimensional torus, and also the Euclidean spaces of dimensions 2 and 3. Most of the results are new and we put the emphasis on the methods, as very little is known on symmetry, rigidity and optimality in the presence of a magnetic field. The most spectacular applications are new magnetic Hardy inequalities in dimensions 2 and 3.