On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau
We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for Rn-valued maps under a suitable convexity assumption on the potential and for H1/2 ∩ L1 boundary data that is non-negative in a fixed direction e ∈ Sn−1. Furthermore, we show that, w...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Société Mathématique de France
2020
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| _version_ | 1797059803082653696 |
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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 | We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for Rn-valued maps under a suitable convexity assumption on the potential and for H1/2 ∩ L1 boundary data that is non-negative in a fixed direction e ∈ Sn−1. Furthermore, we show that, when minimisers are not unique, the set of minimisers is generated from any of its elements using appropriate orthogonal transformations of Rn. We also prove corresponding results for harmonic maps. |
| first_indexed | 2024-03-06T20:09:19Z |
| format | Journal article |
| id | oxford-uuid:2a07763e-d44f-4fbe-86c4-7c5ed783528e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:09:19Z |
| publishDate | 2020 |
| publisher | Société Mathématique de France |
| record_format | dspace |
| spelling | oxford-uuid:2a07763e-d44f-4fbe-86c4-7c5ed783528e2022-03-26T12:22:34ZOn the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-LandauJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a07763e-d44f-4fbe-86c4-7c5ed783528eEnglishSymplectic Elements at OxfordSociété Mathématique de France2020Ignat, RNguyen, LSlastikov, VZarnescu, AWe provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for Rn-valued maps under a suitable convexity assumption on the potential and for H1/2 ∩ L1 boundary data that is non-negative in a fixed direction e ∈ Sn−1. Furthermore, we show that, when minimisers are not unique, the set of minimisers is generated from any of its elements using appropriate orthogonal transformations of Rn. We also prove corresponding results for harmonic maps. |
| spellingShingle | Ignat, R Nguyen, L Slastikov, V Zarnescu, A On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau |
| title | On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau |
| title_full | On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau |
| title_fullStr | On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau |
| title_full_unstemmed | On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau |
| title_short | On the uniqueness of minimisers of Ginzburg-Landau functionals: Sur l'unicité des minimiseurs de la fonctionnelle de Ginzburg-Landau |
| title_sort | on the uniqueness of minimisers of ginzburg landau functionals sur l unicite des minimiseurs de la fonctionnelle de ginzburg landau |
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