We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes into account both the dimensional as well as the magnetic flux contributions. Second, in the three-dimensional Euclidean space, we derive a non-trivial magnetic Hardy inequality for a magnetic field that vanishes at infinity and diverges along a plane.
On the improvement of the Hardy inequality due to singular magnetic fields / Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 45:9(2020), pp. 1202-1212. [10.1080/03605302.2020.1763399]
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli L.;Krejcirik D.
;Laptev A.;
2020
Abstract
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes into account both the dimensional as well as the magnetic flux contributions. Second, in the three-dimensional Euclidean space, we derive a non-trivial magnetic Hardy inequality for a magnetic field that vanishes at infinity and diverges along a plane.| File | Dimensione | Formato | |
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