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Title: Inequalities involving Aharonov–Bohm magnetic potentials in dimensions 2 and 3
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 [Formula: see text] and [Formula: see text].  more » « less
Award ID(s):
1856645
PAR ID:
10219623
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Reviews in Mathematical Physics
ISSN:
0129-055X
Page Range / eLocation ID:
2150006
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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