On the limit $ p\to \infty $ of global minimizers for a p-Ginzburg–Landau-type energy

Almog, Yaniv; Berlyand, Leonid; Golovaty, Dmitry; Shafrir, Itai

On the limit

p \to \infty

of global minimizers for a p-Ginzburg–Landau-type energy

Almog, Yaniv ; Berlyand, Leonid ; Golovaty, Dmitry ; Shafrir, Itai

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013), p. 1159-1174 / Harvested from Numdam

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Résumé

We study the limit $p \to \infty$ of global minimizers for a p-Ginzburg–Landau-type energy The minimization is carried over maps on $ℝ^{2}$ that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on $ℝ^{2}$ and obtain an explicit formula for the limit on $B (0, \sqrt{2})$ . Some generalizations to dimension $N ⩾ 3$ are presented as well.

Publié le : 2013-01-01

MR 3132420 | Zbl 1288.35441

DOI : https://doi.org/10.1016/j.anihpc.2012.12.013

@article{AIHPC_2013__30_6_1159_0,
     author = {Almog, Yaniv and Berlyand, Leonid and Golovaty, Dmitry and Shafrir, Itai},
     title = {On the limit $ p\to \infty $ of global minimizers for a p-Ginzburg--Landau-type energy},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {30},
     year = {2013},
     pages = {1159-1174},
     doi = {10.1016/j.anihpc.2012.12.013},
     mrnumber = {3132420},
     zbl = {1288.35441},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2013__30_6_1159_0}
}

Almog, Yaniv; Berlyand, Leonid; Golovaty, Dmitry; Shafrir, Itai. On the limit $ p\to \infty $ of global minimizers for a p-Ginzburg–Landau-type energy. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) pp. 1159-1174. doi : 10.1016/j.anihpc.2012.12.013. http://gdmltest.u-ga.fr/item/AIHPC_2013__30_6_1159_0/

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