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