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

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

doi:10.1016/j.anihpc.2012.12.013

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) no. 6, pp. 1159-1174.

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.

MR Zbl

DOI : 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 {\protect\emph{p}-Ginzburg{\textendash}Landau-type} energy},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1159--1174},
     publisher = {Elsevier},
     volume = {30},
     number = {6},
     year = {2013},
     doi = {10.1016/j.anihpc.2012.12.013},
     mrnumber = {3132420},
     zbl = {1288.35441},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.12.013/}
}

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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) no. 6, pp. 1159-1174. doi : 10.1016/j.anihpc.2012.12.013. http://www.numdam.org/articles/10.1016/j.anihpc.2012.12.013/

Bibliographie
Cité par

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