  The asymptotic behavior of the micromagnetic free energy governing a
ferromagnetic film is studied as its thickness gets smaller and smaller
compared to its cross section. Here the static Maxwell equations are treated as
a Murat's constant-rank PDE constraint on the energy functional. In contrast to
previous work this approach allows to keep track of the induced magnetic field
without solving the magnetostatic equations. In particular, the mathematical
results of Gioia and James [Proc. R. Soc. Lond. A 453 (1997), pp. 213-223]
regarding convergence of minimizers are recovered by giving a characterization
of the corresponding Gamma-limit.

Analysis of PDEs