We investigate the energy of an isolated magnetized domain Ω ⊂ R n for n = 2 , 3 . In non-dimensionalized variables, the energy given by E ( Ω ) = ∫ R n | ∇ χ Ω | d x + ∫ R n | ∇ h Ω | 2 d x penalizes the interfacial area of the domain as well as the energy of the corresponding magnetostatic field. Here, the magnetostatic potential h Ω is determined by Δ h Ω = ∂ 1 χ Ω , corresponding to uniform magnetization within the domain. We consider the macroscopic regime | Ω | → ∞ , in which we derive compactness and Γ -limit which is formulated in terms of the cross-sectional area of the anisotropically rescaled configuration. We then give the solutions for the limit problems.
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