The existence of Ginzburg-Landau solutions on the plane by a direct variational method
Yang, Yisong
Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994), p. 517-536 / Harvested from Numdam
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Publié le : 1994-01-01
@article{AIHPC_1994__11_5_517_0,
     author = {Yang, Yisong},
     title = {The existence of Ginzburg-Landau solutions on the plane by a direct variational method},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {11},
     year = {1994},
     pages = {517-536},
     mrnumber = {1302278},
     zbl = {0836.35137},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1994__11_5_517_0}
}

Yang, Yisong. The existence of Ginzburg-Landau solutions on the plane by a direct variational method. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) pp. 517-536. http://gdmltest.u-ga.fr/item/AIHPC_1994__11_5_517_0/

[B] M.S. Berger, Nonlinearity and Functional Analysis, Academic, New York, 1977. | MR 488101 | Zbl 0368.47001

[BC] M.S. Berger, Y.Y. Chen, Symmetric Vortices for the Ginzburg-Landau Equations and the Nonlinear Desingularization Phenomenon, J. Funct. Anal., Vol. 82, 259-295, 1989. | MR 987294 | Zbl 0685.46051

[Bo] E.B. Bogomol'Nyi, The Stability of Classical Solutions, Sov. J. Nucl. Phys., Vol. 24, 449-454, 1976. | MR 443719

[DH] P.H. Damgaard, U.M. Heller, Observations of the Meissner Effect in the Lattice Higgs Model, Phys. Rev. Lett., Vol. 60, 1246-1249, 1988.

[GT] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin and New York, 1977. | MR 473443 | Zbl 0361.35003

[GL] V.L. Ginzburg, L.D. Landau, On the Theory of Superconductivity, in Collected Papers of L. D. Landau, D. ter Haar, ed., Pergamon, New York, 1965, 546-568.

[HKP] J. Hong, Y. Kim, P.Y. Pac, Multivortex Solutions of the Abelian Chern-Simons Theory, Phys. Rev. Lett., Vol. 64, 2230-2233, 1990. | MR 1050529 | Zbl 1014.58500

[JLW] R. Jackiw, K. Lee, E.J. Weinberg, Self-dual Chern-Simons Solitons, Phys. Rev. D., Vol. 42, 3488-3499, 1990. | MR 1084551

[JW] R. Jackiw, E.J. Weinberg, Self-dual Chern-Simons Vortices, Phys. Rev. Lett., Vol. 64, 2234-2237, 1990. | MR 1050530 | Zbl 1050.81595

[JT] A. Jaffe, C.H. Taubes, Vortices and Monopoles, Birkhäuser, Boston, 1980. | MR 614447 | Zbl 0457.53034

[L] O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1969. | MR 254401 | Zbl 0184.52603

[P] B.J. Plohr, Ph.D. Thesis, Princeton University, 1980.

[SY] J. Spruck, Y. Yang, The Existence of Non-Topological Solitons in the Self-Dual Chern-Simons Theory, Commun. Math. Phys., Vol. 149, 361-376, 1992. | MR 1186034 | Zbl 0760.53063

[T1] C.H. Taubes, Arbitrary N-vortex Solutions to the First Order Ginzburg-Landau Equations, Commun. Math. Phys., Vol. 72, 277-292, 1980. | MR 573986 | Zbl 0451.35101

[T2] C.H. Taubes, On the Equivalence of the First and Second Order Equations for Gauge Theories, Commun. Math. Phys., Vol. 75, 207-227, 1980. | MR 581946 | Zbl 0448.58029

[Y1] Y. Yang, Existence, Regularity, and Asymptotic Behavior of the Solutions to the Ginzburg-Landau Equations on R3, Commun. Math. Phys., Vol. 123, 147-161, 1989. | MR 1002036 | Zbl 0678.35086

[Y2] Y. Yang, On the Abelian Higgs models with sources, J. Math. Pures et Appl., Vol. 70, 325-344, 1991. | MR 1113815 | Zbl 0662.35115