3D-2D asymptotic analysis for micromagnetic thin films
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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 Ω ε =ω×(-ε,ε), ω 2 , whose energy is given by

ε (m ¯)=1 ε Ω ε W(m ¯,m ¯)+1 2u ¯·m ¯dx
subject to
div(-u ¯+m ¯χ Ω ε )=0on 3 ,
and to the constraint
|m ¯|=1onΩ ε ,
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
Keywords: $\Gamma $-limit, thin films, micromagnetics, relaxation of constrained functionals
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     title = {3D-2D asymptotic analysis for micromagnetic thin films},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {489--498},
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     volume = {6},
     year = {2001},
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     url = {http://archive.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, Volume 6 (2001), pp. 489-498. http://archive.numdam.org/item/COCV_2001__6__489_0/

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