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 Ic tends to zero. Surprisingly, we show a connection between the asymptotic behavior of the given double vortex as k --> 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.

Double vortex condensates in the Chern-Simons-Higgs theory

NOLASCO, MARGHERITA;
1999

Abstract

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 Ic tends to zero. Surprisingly, we show a connection between the asymptotic behavior of the given double vortex as k --> 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/21140
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 127
  • ???jsp.display-item.citation.isi??? 135
social impact