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A Ginzburg–Landau problem with weight having minima on the boundary

Published online by Cambridge University Press:  14 November 2011

Anne Beaulieu  and
Rejeb Hadiji
Anne Beaulieu
Affiliation:
Equipe d'Analyse et de Mathematiques Appliquees, Université de Marne-la-Vallée, Cité Descartes-5, bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France
Rejeb Hadiji
Affiliation:
CMLA, ENS de Cachan, 61, avenue du Président Wilson, 94235 Cachan Cedex, France; andUniversité de Picardie, 33, rue Saint-Leu, 80039 Amiens Cedex 01, France
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Extract

In this paper, we study the following Ginzburg–Landau functional:

where (G, C), and p is a smooth bounded and non-negative map, having minima on the boundary of Ḡ. We give the location of the singularities in the case where the degree around each singularity is equal to 1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1181 - 1215
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

1Adams, R. A.. Sobolev Spaces (New York: Academic Press, 1975).Google Scholar
2Andre, N. and Shafrir, I.. Minimization of the Ginzburg–Landau functional with weight. C. R. Acad. Sci. Paris, Sér. I 321 (1995), 999–1004.Google Scholar
3Andre, N. and Shafrir, I.. Asymptotic behavior minimizers for the Ginzburg–Landau functional with weight, Parts I and II. Arch. Rational Mech. Anal. (to appear).Google Scholar
4Beaulieu, A. and Hadiji, R.. Asymptotics for minimizers of a class of Ginzburg–Landau equations with weight. C. R. Acad. Sci. Paris, Sér. I 320 (1995), 181–6.Google Scholar
5Beaulieu, A. and Hadiji, R.. On a class of Ginzburg–Landau equations with weight. Panamer. Math. J. 4(1995), 1–33.Google Scholar
6Beaulieu, A. and Hadiji, R.. Ginzburg–Landau equations and Pohozaev identity. In Progress in Partial Differential Equations. The Metz Survey No. 4, 345 (Harlow, Longman, 1996).Google Scholar
7Bethuel, F., Brezis, H. and Helein, F.. Asymptotics for the minimization of a Ginzburg–Landau functional. Calc. Var. Partial Differential Equations (1993), 123–148.CrossRefGoogle Scholar
8Bethuel, F., Brezis, H. and Helein, F.. Ginzburg–Landau-Vortices (Boston: Birkhaüser, 1994).CrossRefGoogle Scholar
9Brezis, H.. Lecture note on Ginzburg–Landau vortices (Scuola Normale Superiore, Pisa, 1995).Google Scholar
10Brezis, H., Merle, F. and Rivière, T.. Quantization effects for − Δu = u(1 − \u\2) in ℝ2. Arch. Rational Mech. Anal. 126 (1994), 35–58.CrossRefGoogle Scholar
11Comte, M. and Mironescu, P.. The behavior of a Ginzburg–Landau minimzer near its zeros. Calc. Var. Partial Differential Equations 4 (1996), 323–40.CrossRefGoogle Scholar
12Du, Q. and Gunzburger, M.. A model for superconducting thin films having variable thickness. Phys. D 69 (1994), 215–31.CrossRefGoogle Scholar
13Han, Z. C. and Shafrir, I.. Lower bounds for the energy of S1-valued maps in perforated domains. J. Anal. Math. 66 (1995), 295–305.CrossRefGoogle Scholar
14Struwe, M.. On the asymptotic behavior of minimizers of the Ginzburg–Landau model in 2 dimensions. Differential Integral Equations 7 (1994), 1613–24; erratum, Differential Integral Equations 8(1995), 124.CrossRefGoogle Scholar