Fabian Portmann: Magnetic Hardy Inequalities

We study the magnetic Dirichlet form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic field does not vanish identically, then the classical lower bound given by Hardy is improved by a non-negative potential depending on properties of the magnetic field. This is joint work with Tomas Ekholm.