On the Laplace operator with a weak magnetic field in exterior domains
On the Laplace operator with a weak magnetic field in exterior domains
We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak magnetic field limit. For the exterior of a star-shaped domain, we obtain an asymptotic upper …