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{\bf [Thin-film $\Gamma$-limit of the micromagnetic \\free energy}

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{Carolin Kreisbeck}\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
Pittsburgh, PA~15213, USA\\
carolink@andrew.cmu.edu

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{Filip Rindler}\\
Mathematical Institute\\
 University of Oxford\\
 24--29 St Giles'\\
Oxford OX1 3LB, United Kingdom\\
{rindler@maths.ox.ac.uk}
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\noindent {\bf abstract}: 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~[\textit{Proc.\ R.\
  Soc.\ Lond.\ A} 453 (1997), pp. 213--223] regarding convergence of
minimizers are extended by giving a full characterization of the corresponding
$\Gamma$-limit.


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