%0 Journal Article
%T Relativistic Hardy inequalities in magnetic fields
%A Luca Fanelli
%A Luis Vega
%A Nicola Visciglia
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s10955-014-0915-0
%X We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best constant as in the free case. This leaves naturally open an interesting question whether there exist magnetic fields for which a Hardy inequality with a better constant than the usual one, in connection with the well known diamagnetic phenomenon arising in non-relativistic models.
%U http://arxiv.org/abs/1309.3746v1