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

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.

Locations

• Communications in Partial Differential Equations - View
• arXiv (Cornell University) - View - PDF
• BIRD (Basque Center for Applied Mathematics) - View - PDF
• LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF
• IRIS Research product catalog (Sapienza University of Rome) - View - PDF