Another approach to the thin-film Γ-limit of the micromagnetic free energy in the regime of small samples

Kreisbeck, Carolin

doi:10.1090/S0033-569X-2012-01323-5

Another approach to the thin-film $\Gamma$-limit of the micromagnetic free energy in the regime of small samples

Author: Carolin Kreisbeck
Journal: Quart. Appl. Math. 71 (2013), 201-213
MSC (2010): Primary 49J45, 35E99, 35Q61, 74F15, 74K35
DOI: https://doi.org/10.1090/S0033-569X-2012-01323-5
Published electronically: August 28, 2012
MathSciNet review: 3087419
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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 us 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.

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