On the limit p of global minimizers for a p-Ginzburg–Landau-type energy
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 6, p. 1159-1174
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consulter l'article sur le site de la revue
We study the limit p of global minimizers for a p-Ginzburg–Landau-type energy The minimization is carried over maps on 2 that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on 2 and obtain an explicit formula for the limit on B(0,2). Some generalizations to dimension N3 are presented as well.
@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},
     publisher = {Elsevier},
     volume = {30},
     number = {6},
     year = {2013},
     pages = {1159-1174},
     doi = {10.1016/j.anihpc.2012.12.013},
     zbl = {1288.35441},
     mrnumber = {3132420},
     language = {en},
     url = {http://www.numdam.org/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) no. 6, pp. 1159-1174. doi : 10.1016/j.anihpc.2012.12.013. http://www.numdam.org/item/AIHPC_2013__30_6_1159_0/

[1] Y. Almog, L. Berlyand, D. Golovaty, I. Shafrir, Global minimizers for a p-Ginzburg–Landau-type energy in 2 , J. Funct. Anal. 256 (2009), 2268-2290 | MR 2498765 | Zbl 1160.49003

[2] Y. Almog, L. Berlyand, D. Golovaty, I. Shafrir, Radially symmetric minimizers for a p-Ginzburg–Landau type energy in 2 , Calc. Var. Partial Differential Equations 42 (2011), 517-546 | MR 2846265 | Zbl 1237.35149

[3] E.F. Beckenbach, R. Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge vol. 30, Springer-Verlag, New York (1965) | MR 192009 | Zbl 0513.26003

[4] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer (2011) | MR 2759829 | Zbl 1220.46002

[5] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, Springer-Verlag, Berlin (2001) | Zbl 1042.35002 | Zbl 0691.35001

[6] T. Iwaniec, G. Martin, Geometric Function Theory and Non-linear Analysis, Oxford Mathematical Monographs, The Clarendon Press/Oxford University Press, New York (2001) | MR 1859913 | Zbl 1045.30011

[7] P. Mironescu, Les minimiseurs locaux pour lʼéquation de Ginzburg–Landau sont à symétrie radiale, C. R. Acad. Sci. Paris, Sér. I Math. 323 (1996), 593-598 | MR 1411048 | Zbl 0858.35038

[8] E. Sandier, Locally minimising solutions of -Δu=u(1-|u| 2 ) in 𝐑 2 , Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), 349-358 | MR 1621347 | Zbl 0905.35018