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...
| Main Authors: | , , , |
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| Format: | Journal article |
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Elsevier
2018
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| _version_ | 1797052447988908032 |
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| author | Ignat, R Nguyen, L Slastikov, V Zarnescu, A |
| author_facet | Ignat, R Nguyen, L Slastikov, V Zarnescu, A |
| author_sort | Ignat, R |
| collection | OXFORD |
| description | 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 . |
| first_indexed | 2024-03-06T18:31:42Z |
| format | Journal article |
| id | oxford-uuid:09df3f36-f967-4c12-b3c1-cdbde5fdad1e |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:31:42Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:09df3f36-f967-4c12-b3c1-cdbde5fdad1e2022-03-26T09:20:39ZUniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:09df3f36-f967-4c12-b3c1-cdbde5fdad1eSymplectic Elements at OxfordElsevier2018Ignat, RNguyen, LSlastikov, VZarnescu, AFor 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 . |
| spellingShingle | Ignat, R Nguyen, L Slastikov, V Zarnescu, A Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$ |
| title | Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$ |
| title_full | Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$ |
| title_fullStr | Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$ |
| title_full_unstemmed | Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$ |
| title_short | Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$ |
| title_sort | uniqueness of degree one ginzburg landau vortex in the unit ball in dimensions n geq 7 |
| work_keys_str_mv | AT ignatr uniquenessofdegreeoneginzburglandauvortexintheunitballindimensionsngeq7 AT nguyenl uniquenessofdegreeoneginzburglandauvortexintheunitballindimensionsngeq7 AT slastikovv uniquenessofdegreeoneginzburglandauvortexintheunitballindimensionsngeq7 AT zarnescua uniquenessofdegreeoneginzburglandauvortexintheunitballindimensionsngeq7 |