  In this paper we prove a two-term asymptotic formula for for the spectral
counting function for a 2D magnetic Schr\"odinger operator on a domain (with
Dirichlet boundary conditions) in a semiclassical limit and with strong
magnetic field. By scaling, this is equivalent to a thermodynamic limit of a 2D
Fermi gas submitted to a constant external magnetic field.
  The original motivation comes from a paper by H. Kunz in which he studied,
among other things, the boundary correction for the grand-canonical pressure
and density of such a Fermi gas. Our main theorem yields a rigorous proof of
the formulas announced by Kunz. Moreover, the same theorem provides several
other results on the integrated density of states for operators of the type
$(-ih\nabla- \mu {\bf A})^2$ in $L^2({\Omega})$ with Dirichlet boundary
conditions.
