Averaging of magnetic fields and applications

In this paper, we estimate the magnetic Laplacian energy norm in appropriate planar domains under a weak regularity hypothesis on field. Our main contribution is an averaging estimate, valid small cells, allowing us to pass from non-uniform uniform fields. As matter of application, derive new upper and lower bounds lowest eigenvalue Dirichlet which match regime large field intensity. Furthermore, our technique allows nonlinear Ginzburg–Landau energy, as byproduct, yields non-Gaussian trial state for Laplacian.