3D-2D asymptotic analysis for micromagnetic thin films
ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 489-498.

Γ-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure Ωε=ω×(-ε,ε), ω⊂ℝ2, whose energy is given by

ℰε(m¯)=1ε∫ΩεW(m¯,∇m¯)+12∇u¯·m¯dx
subject to
div(-∇u¯+m¯χΩε)=0onℝ3,
and to the constraint
|m¯|=1onΩε,
where W is any continuous function satisfying p-growth assumptions with p>1. Partial results are also obtained in the case p=1, under an additional assumption on W.

Classification : 35E99, 35M10, 49J45, 74K35
Mots-clés : Γ-limit, thin films, micromagnetics, relaxation of constrained functionals 
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     author = {Alicandro, Roberto and Leone, Chiara},
     title = {3D-2D asymptotic analysis for micromagnetic thin films},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {489--498},
     publisher = {EDP-Sciences},
     volume = {6},
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     mrnumber = {1836053},
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     url = {https://www.numdam.org/item/COCV_2001__6__489_0/}
}
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Alicandro, Roberto; Leone, Chiara. 3D-2D asymptotic analysis for micromagnetic thin films. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 489-498. https://www.numdam.org/item/COCV_2001__6__489_0/

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