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 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.
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Received: March 3, 1998 / Accepted October 23, 1998
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Nolasco, M., Tarantello, G. Double vortex condensates in the Chern-Simons-Higgs theory. Calc Var 9, 31–94 (1999). https://doi.org/10.1007/s005260050132
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DOI: https://doi.org/10.1007/s005260050132