The existence of Ginzburg-Landau solutions on the plane by a direct variational method

Yisong Yang

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 5, page 517-536
  • ISSN: 0294-1449

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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 11.5 (1994): 517-536. <http://eudml.org/doc/78342>.

@article{Yang1994,
author = {Yang, Yisong},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {minimization; Ginzburg-Landau equations; Sobolev inequality; modified energy; Ginzburg-Landau energy},
language = {eng},
number = {5},
pages = {517-536},
publisher = {Gauthier-Villars},
title = {The existence of Ginzburg-Landau solutions on the plane by a direct variational method},
url = {http://eudml.org/doc/78342},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Yang, Yisong
TI - The existence of Ginzburg-Landau solutions on the plane by a direct variational method
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 5
SP - 517
EP - 536
LA - eng
KW - minimization; Ginzburg-Landau equations; Sobolev inequality; modified energy; Ginzburg-Landau energy
UR - http://eudml.org/doc/78342
ER -

References

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  1. [B] M.S. Berger, Nonlinearity and Functional Analysis, Academic, New York, 1977. Zbl0368.47001MR488101
  2. [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. Zbl0685.46051MR987294
  3. [Bo] E.B. Bogomol'nyi, The Stability of Classical Solutions, Sov. J. Nucl. Phys., Vol. 24, 449-454, 1976. MR443719
  4. [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. 
  5. [GT] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin and New York, 1977. Zbl0361.35003MR473443
  6. [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. 
  7. [HKP] J. Hong, Y. Kim, P.Y. Pac, Multivortex Solutions of the Abelian Chern-Simons Theory, Phys. Rev. Lett., Vol. 64, 2230-2233, 1990. Zbl1014.58500MR1050529
  8. [JLW] R. Jackiw, K. Lee, E.J. Weinberg, Self-dual Chern-Simons Solitons, Phys. Rev. D., Vol. 42, 3488-3499, 1990. MR1084551
  9. [JW] R. Jackiw, E.J. Weinberg, Self-dual Chern-Simons Vortices, Phys. Rev. Lett., Vol. 64, 2234-2237, 1990. Zbl1050.81595MR1050530
  10. [JT] A. Jaffe, C.H. Taubes, Vortices and Monopoles, Birkhäuser, Boston, 1980. Zbl0457.53034MR614447
  11. [L] O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1969. Zbl0184.52603MR254401
  12. [P] B.J. Plohr, Ph.D. Thesis, Princeton University, 1980. 
  13. [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. Zbl0760.53063MR1186034
  14. [T1] C.H. Taubes, Arbitrary N-vortex Solutions to the First Order Ginzburg-Landau Equations, Commun. Math. Phys., Vol. 72, 277-292, 1980. Zbl0451.35101MR573986
  15. [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. Zbl0448.58029MR581946
  16. [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. Zbl0678.35086MR1002036
  17. [Y2] Y. Yang, On the Abelian Higgs models with sources, J. Math. Pures et Appl., Vol. 70, 325-344, 1991. Zbl0662.35115MR1113815

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