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Variational methods for Ginzburg-Landau equations

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Calculus of Variations and Geometric Evolution Problems

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References

  • [A] L. Almeida, Thesis.

    Google Scholar 

  • [AB1] L. Almeida and F. Bethuel, Multiplicity results for the Ginzburg-Landau equation in presence of symmetries, to appear in Houston J. of Math.

    Google Scholar 

  • [AB2] L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equation, preprint.

    Google Scholar 

  • [BBH] F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau vortices, Birkhaüser, (1994).

    Google Scholar 

  • [BBH2] F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. and PDE, 1, (1993), 123–148.

    Article  MathSciNet  MATH  Google Scholar 

  • [BCP] P. Bauman, N. Carlson and D. Philipps, On the zeroes of solutions to Ginzburg-Landau type systems, to appear.

    Google Scholar 

  • [BHe] F. Bethuel and B. Helffer, preprint.

    Google Scholar 

  • [BR] F. Bethuel and T. Rivière, A minimization problem related to superconductivity, Annales IHP, Analyse Non Linéaire, (1995), 243–303.

    Google Scholar 

  • [BR2] F. Bethuel and T. Rivière, Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité, Séminaire Ecole Polytechnique 1993–1994, exposé no XV.

    Google Scholar 

  • [BS] F. Bethuel and J.C. Saut, Travelling waves for the Gross-Putaevskii equation, preprint.

    Google Scholar 

  • [DF] M. Del Pino and P. Felmer, preprint.

    Google Scholar 

  • [GL] V. Ginzburg and L. Landau, On the theory of superconductivity, Zh Eksper. Teoret. Fiz, 20 (1950) 1064–1082.

    Google Scholar 

  • [JMZ] S. Jimbo, Y. Morita and J. Zhaï, Ginzburg-Landau equation and stable steady state solutions in a non-trivial domain, preprint.

    Google Scholar 

  • [JS] LR.L. Jerrard and H.M. Soner, Asymptotic heat-flow dynamics for Ginzburg-Landau vortices, preprint, (1995).

    Google Scholar 

  • [Li1] F.H. Lin, Solutions of Ginzburg-Landau equations and critical points of the renormalized energy, Annales IHP, Analyse Non Linéaire, 12 (1995) 599–622.

    MathSciNet  MATH  Google Scholar 

  • [Li2] F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices, to appear in CPAM.

    Google Scholar 

  • [Mcd] D. Mac Duff, Configuration spaces of positive and negative particles, Topology, 14 (1974) 91–107.

    Article  MathSciNet  Google Scholar 

  • [Mi1] P. Mironescu, On the stability of radial solutions of the Ginzburg-Landau equation, J. Funct. Anal., 130 (1995) 334–344.

    Article  MathSciNet  MATH  Google Scholar 

  • [Mi2] P. Mironescu, Les minimiseurs locaux pour l'équation de Ginzburg-Landau sont à symétrie radiale, C. R. Acad Sci. Paris, 6, (323), 593–598.

    Google Scholar 

  • [PN] L. Pismen and A. Nepomnyashechy, Stability of vortex rings in a model of superflow, Physica D, (1993) 163–171.

    Google Scholar 

  • [RS] J. Rubinstein and P. Sternberg, Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents, to appear.

    Google Scholar 

  • [Sta] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Presses Université de Montréal (1966).

    Google Scholar 

  • [Str] M. Struwe, On the asymptotic behavior of the Ginzburg-Landau model in 2 dimensions, J. Diff. Int. Equ., 7 (1994) 1613–1324; Erratum 8, (1995) 224.

    MathSciNet  MATH  Google Scholar 

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Stefan Hildebrandt Michael Struwe

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© 1999 Springer-Verlag

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Bethuel, F. (1999). Variational methods for Ginzburg-Landau equations. In: Hildebrandt, S., Struwe, M. (eds) Calculus of Variations and Geometric Evolution Problems. Lecture Notes in Mathematics, vol 1713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092668

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  • DOI: https://doi.org/10.1007/BFb0092668

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  • Print ISBN: 978-3-540-65977-8

  • Online ISBN: 978-3-540-48813-2

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