Diana Barseghyan

The aim of the work is to derive spectral estimates into several classes of magnetic
systems. They include three-dimensional regions with Dirichlet boundary as well
as a particle in R^3 confined by a local change of the magnetic field. We establish
two-dimensional Berezin-Li-Yau and Lieb- Thirring-type bounds in the presence of
magnetic fields and, using them, get three-dimensional estimates for the eigenvalue
moments of the corresponding magnetic Laplacians.