Double vortex condensates in the Chern-Simons-Higgs theory

  • Margherita Nolasco
  • Gabriella Tarantello

DOI: 10.1007/s005260050132

Cite this article as:
Nolasco, M. & Tarantello, G. Calc Var (1999) 9: 31. doi:10.1007/s005260050132


For a selfdual model introduced by Hong-Kim-Pac [18] and Jackiw-Weinberg [19] we study the existence of double vortex-condensates“bifurcating” from the symmetric vacuum state as the Chern-Simons coupling parameter k tends to zero. Surprisingly, we show a connection between the asymptotic behavior of the given double vortex as \(k \to 0^{+}\) with the existence of extremal functions for a Sobolev inequality of the Moser-Trudinger's type on the flat 2-torus ([22], [1] and [15]). In fact, our construction yields to a “best” minimizing sequence for the (non-coercive) associated extremal problem, in the sense that, the infimum is attained if and only if the given minimizing sequence admits a convergent subsequence.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Margherita Nolasco
    • 1
  • Gabriella Tarantello
    • 2
  1. 1. Dipartimento di Matematica, Università di L'Aquila, Via Vetoio, Coppito, I-67010 L'Aquila, Italy (e-mail: IT
  2. 2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy (e-mail: IT

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