# Abstract

We prove that the two dimensional free magnetic Schrödinger operator,
with a fixed constant magnetic field and Dirichlet boundary conditions
on a planar domain with a given area, attains its smallest possible eigenvalue
if the domain is a disk. This generalizes the classical
Faber-Krahn inequality for magnetic fields. The result is
used to determine the low energy asymptotic behaviour
of the integrated density of states of the magnetic Schrödinger
operator with Poissonian random potential.
Heinz Siedentop