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G. Di Fratta:
"Micromagnetics of curved thin films";
in: "ASC Report 17/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 21.

n this paper, we aim at a reduced 2d-model describing the observable states of the magnetization in curved thin films. Under some technical assumptions on the geometry of the thin-film, it is well-known that the demagnetizing field behaves like the projection of the magnetization on the normal to the thin film. We remove these assumptions and show that the result holds for a broader class of surfaces; in particular, for compact surfaces. We treat both the stationary case, governed by the micromagnetic energy functional and the time-dependent case driven by the Landau-Lifshitz-Gilbert equation.

Micromagnetics, Landau-Lifshitz-Gilbert equation, curved thin films, Γ-convergence

http://www.asc.tuwien.ac.at/preprint/2020/asc17x2020.pdf