We study the asymptotic behaviour, as ε → 0, ofa sequence {uε} of minimizers for the Ginzburg-Landau functional which satisfies local energy bounds of order | log ε |. The jacobians Juε are shown to converge, in a suitable sense and up to subsequences, to an area minimizing minimal surface of codimension2. This is achieved without assumptions on the globalenergy of the sequence or on the boundary data, and holds evenfor unbounded domains. The proof is based on an improvedversion of the Γ -convergence results from [3].
Convergence of minimizers with local energy bounds for the Ginzburg-Landau functionals
BALDO, Sisto;ORLANDI, Giandomenico;
2009-01-01
Abstract
We study the asymptotic behaviour, as ε → 0, ofa sequence {uε} of minimizers for the Ginzburg-Landau functional which satisfies local energy bounds of order | log ε |. The jacobians Juε are shown to converge, in a suitable sense and up to subsequences, to an area minimizing minimal surface of codimension2. This is achieved without assumptions on the globalenergy of the sequence or on the boundary data, and holds evenfor unbounded domains. The proof is based on an improvedversion of the Γ -convergence results from [3].
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