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arXiv · 1807.04430

On the improvement of the Hardy inequality due to singular magnetic fields

Luca Fanelli·David Krejcirik·Ari Laptev·Luis Vega
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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.

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Luca Fanelli, David Krejcirik, Ari Laptev, Luis Vega. 2018-07-12. On the improvement of the Hardy inequality due to singular magnetic fields. https://arxiv.org/abs/1807.04430

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