Laszlo Erdos
Rayleigh-type Isoperimetric Inequality with a Homogeneous Magnetic Field
The paper is published: \jour Calc. Var. and PDE\vol 4\yr 1996\pages 283--292

MSC:

35P15 Estimation of eigenvalues, upper and lower bounds

49R05 Variational approach to eigenvalues

35J10 Schrodinger operator, See also {35Pxx}

Abstract: We prove that the two dimensional free magnetic Schr\"o\-dinger operator,
with a fixed constant magnetic field and Dirichlet boundary conditions
on a planar domain with a given area, attains its smallest possible eigenvalue
if the domain is a disk. We also give some
rough bounds on the lowest magnetic eigenvalue of the disk.

Keywords: smallest eigenvalue, magnetic Schroedinger operator