Sharp upper bounds for a singular perturbation problem related to micromagnetics
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 673-701.

We construct an upper bound for the following family of functionals {E ε } ε>0 , which arises in the study of micromagnetics:

E ε (u)= Ω ε|u| 2 +1 ε 2 |H u | 2 .
Here Ω is a bounded domain in 2 , uH 1 (Ω,S 1 ) (corresponding to the magnetization) and H u , the demagnetizing field created by u, is given by
div (u ˜+H u )=0in 2 , curl H u =0in 2 ,
where u ˜ is the extension of u by 0 in 2 Ω. Our upper bound coincides with the lower bound obtained by Rivière and Serfaty.

Classification : 49J45, 35B25, 35J20
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Poliakovsky, Arkady. Sharp upper bounds for a singular perturbation problem related to micromagnetics. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 673-701. http://archive.numdam.org/item/ASNSP_2007_5_6_4_673_0/

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