Bethuel, Fabrice; Rivière, Tristan Vortices for a variational problem related to superconductivity. (English) Zbl 0842.35119 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 12, No. 3, 243-303 (1995). Summary: We study minimizers of Ginzburg-Landau functionals, which depend on a parameter \(\varepsilon\). These functionals appear in superconductivity and two dimensional abelian Higgs models. We study the asymptotic limit, as \(\varepsilon \to 0\), of minimizers and show that the limiting configuration has vortices, which have topological degree one. Cited in 1 ReviewCited in 53 Documents MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 35A15 Variational methods applied to PDEs 82D55 Statistical mechanics of superconductors Keywords:Ginzburg-Landau equation; minimizers of Ginzburg-Landau functionals; superconductivity; Higgs models; vortices × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] Bethuel, F.; Brezis, H.; Hélein, F., Asymptotics for the minimization of a Ginzburg-Landau functional, Calculus of Variations, Vol. I, 123-148 (1993) · Zbl 0834.35014 [2] Bethuel, F.; Brezis, H.; Hélein, F., Ginzburg-Landau Vortices (1993), Birkhäuser · Zbl 0783.35014 [3] Bethuel, F.; Brezis, H.; Hélhn, F., Limite singulière pour la minimisation de fonctionnelles du type Ginzburg-Landau, C. R. Acad. Sci. Paris, Vol. 314, 891-895 (1992) · Zbl 0773.49003 [7] Boutetde Monvel-Berthier, A.; Georgescu, V.; Purice, R., Sur un problème aux limites de la théorie de Ginzburg-Landau, C. R. Acad. Sci. Paris, Vol. 307, 55-58 (1988) · Zbl 0696.35058 [8] Comtet, A.; Gibbons, G. W., Bogomol’nyi bounds for cosmic strings, Nucl. Phys. B, Vol. 299, 719-733 (1988) [9] Du, Q.; Gunzburger, M.; Peterson, J., Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Review, Vol. 34, 45-81 (1992) · Zbl 0787.65091 [10] Grisvard, P., Elliptic Problems in non-smooth domains (1985), Pitman: Pitman Marshfields, Mass · Zbl 0695.35060 [11] Jaffe, A.; Taubes, C., Vortices and Monopoles (1980), Birkhäuser · Zbl 0457.53034 [12] Saint-James, D.; Sarma, G.; Thomas, E. J., Type II Superconductivity (1969), Pergamon Press [14] Spruck, J.; Yang, Y., On multivortices in the electroweak theory II: existence of Bogomol’nyi solutions in, Comm. Math. Phys., Vol. 144, 215-234 (1992) · Zbl 0748.53060 [16] Yang, Y., Boundary value problems of the Ginzburg-Landau equations, Proc. Roy. Soc. Edinburgh, Vol. 114 A, 355-365 (1990) · Zbl 0708.35074 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.