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Relativistic Hardy Inequalities in Magnetic Fields |
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| Authors: | Luca Fanelli Luis Vega Nicola Visciglia |
| Institution: | 1. Dip. di Matematica “G. Castelnuovo”, SAPIENZA Università di Roma, P.le A.Moro 5, 00185?, Rome, Italy 2. Dep. de Matemáticas, Universidad del País Vasco, Apartado 644, 48080?, Bilbao, Spain 3. Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, 48009?, Bilbao, Spain 4. Dip. di Matematica “L. Tonelli”, Università Degli Studi di Pisa, Largo Bruno Pontecorvo 5, 56127?, Pisa, Italy |
| Abstract: | 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. |
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