"Eigenvalue bounds for the magnetic Laplacians and Schroedinger operators"

We are going to derive spectral estimates for several classes of magnetic Lapla-cians. They include the magnetic Laplacian on three-dimensional regions with Dirichlet boundary conditions as well as the magnetic Laplacian dened in R3 with the local change of the magnetic eld. We establish two-dimensional Berezin- Li-Yau and Lieb-Thirring-type bounds in the presence of constant magnetic elds and, using them, get three-dimensional estimates for the eigenvalue moments of the corresponding magnetic Laplacians. Also we derive separately the Lieb-Thirring bounds for the magnetic Schroeodinger operators dened on two dimensional circle with radially symmetric magnetic eld and electric potentials.