Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$
For ε > 0, we consider the Ginzburg-Landau functional for R N -valued maps defined in the unit ball BN ⊂ R N with the vortex boundary data x on ∂BN . In dimensions N ≥ 7, we prove that for every ε > 0, there exists a unique global minimizer uε of this problem; moreover, uε is symmetric...
| Váldodahkkit: | , , , |
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| Materiálatiipa: | Journal article |
| Almmustuhtton: |
Elsevier
2018
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| Čoahkkáigeassu: | For ε > 0, we consider the Ginzburg-Landau functional for R N -valued maps defined in the unit ball BN ⊂ R N with the vortex boundary data x on ∂BN . In dimensions N ≥ 7, we prove that for every ε > 0, there exists a unique global minimizer uε of this problem; moreover, uε is symmetric and of the form uε(x) = fε(|x|) x |x| for x ∈ BN . |
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