We revisit the basic variational formulation of the minimization problem
associated with the micromagnetic energy, with an emphasis on the treatment of
the stray field contribution to the energy, which is intrinsically non-local.
Under minimal assumptions, we establish three distinct variational principles
for the stray field energy: a minimax principle involving magnetic scalar
potential and two minimization principles involving magnetic vector potential.
We then apply our formulations to the dimension reduction problem for thin
ferromagnetic shells of arbitrary shapes
