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Relativistic Hardy inequalities in magnetic fields

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.

preprint2013arXivOpen access
Luca FanelliLuis VegaNicola Visciglia
math.APmath-phmath.MP
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Luca FanelliLuis VegaNicola Visciglia

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