On the lowest eigenvalue of the Dirichlet Laplacian with magnetic field in a Sobolev space

After reviewing the known leading strong field asymptotics of the Dirichlet magnetic Laplcian, the focus will be on the case where the magnetic field is in a Sobolev space. The asymptotics are then derived via an averaging mechanism. The case of the Neumann boundary condition and other cases of less regular magnetic fields will be discussed too.