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 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
Mots clés : Γ-limit, thin films, micromagnetics, relaxation of constrained functionals
@article{COCV_2001__6__489_0,
     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},
     year = {2001},
     zbl = {0989.35009},
     mrnumber = {1836053},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2001__6__489_0/}
}
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. http://www.numdam.org/item/COCV_2001__6__489_0/

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