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, p. 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
@article{ASNSP_2007_5_6_4_673_0,
     author = {Poliakovsky, Arkady},
     title = {Sharp upper bounds for a singular perturbation problem related to micromagnetics},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {4},
     year = {2007},
     pages = {673-701},
     zbl = {1150.49006},
     mrnumber = {2394415},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2007_5_6_4_673_0}
}
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://www.numdam.org/item/ASNSP_2007_5_6_4_673_0/

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