Eigenvalues variations for Aharonov-Bohm operators

We study how the eigenvalues of a magnetic Schrödinger operator of Aharonov-Bohm type depend on the singularities of its magnetic potential. We consider a magnetic potential defined everywhere in the plane except at a finite number of singularities, so that the associated magnetic field is zero. On a fixed planar domain, we define the corresponding magnetic Hamiltonian with Dirichlet boundary conditions, and study its eigenvalues as functions of the singularities. We prove that these functions are continuous, and in some cases even analytic. We sketch the connection of this eigenvalue problem to the problem of finding spectral minimal partitions of the domain.