A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$
Abstract In this paper we consider an energy functional depending on the norm of the gradient and seek to extremise it over an admissible class of Sobolev maps defined on an annulus and taking values on the unit sphere whilst satisfying suitable boundary conditions. We establish the existence of an...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-12-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0917-3 |
| _version_ | 1818906400009486336 |
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| author | Stuart Day Ali Taheri |
| author_facet | Stuart Day Ali Taheri |
| author_sort | Stuart Day |
| collection | DOAJ |
| description | Abstract In this paper we consider an energy functional depending on the norm of the gradient and seek to extremise it over an admissible class of Sobolev maps defined on an annulus and taking values on the unit sphere whilst satisfying suitable boundary conditions. We establish the existence of an infinite family of solutions with certain symmetries to the associated nonlinear Euler-Lagrange system in even dimensions and discuss the stability of such extremisers by way of examining the positivity of the second variation of the energy at these solutions. |
| first_indexed | 2024-12-19T21:38:37Z |
| format | Article |
| id | doaj.art-f8f2c2e9ab484b1a94e6d8317d2a6a47 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-19T21:38:37Z |
| publishDate | 2017-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-f8f2c2e9ab484b1a94e6d8317d2a6a472022-12-21T20:04:44ZengSpringerOpenBoundary Value Problems1687-27702017-12-012017111710.1186/s13661-017-0917-3A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$Stuart Day0Ali Taheri1Department of Mathematics, University of SussexDepartment of Mathematics, University of SussexAbstract In this paper we consider an energy functional depending on the norm of the gradient and seek to extremise it over an admissible class of Sobolev maps defined on an annulus and taking values on the unit sphere whilst satisfying suitable boundary conditions. We establish the existence of an infinite family of solutions with certain symmetries to the associated nonlinear Euler-Lagrange system in even dimensions and discuss the stability of such extremisers by way of examining the positivity of the second variation of the energy at these solutions.http://link.springer.com/article/10.1186/s13661-017-0917-3spherical whirlssymmetriesgeneralised sphere-valued harmonic mapsSO ( n ) $\mathbf{SO}(n)$maximal tori and conjugacysecond energy variations |
| spellingShingle | Stuart Day Ali Taheri A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$ Boundary Value Problems spherical whirls symmetries generalised sphere-valued harmonic maps SO ( n ) $\mathbf{SO}(n)$ maximal tori and conjugacy second energy variations |
| title | A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$ |
| title_full | A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$ |
| title_fullStr | A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$ |
| title_full_unstemmed | A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$ |
| title_short | A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO ( n ) $\mathbf{SO}(n)$ |
| title_sort | class of extremising sphere valued maps with inherent maximal tori symmetries in so n mathbf so n |
| topic | spherical whirls symmetries generalised sphere-valued harmonic maps SO ( n ) $\mathbf{SO}(n)$ maximal tori and conjugacy second energy variations |
| url | http://link.springer.com/article/10.1186/s13661-017-0917-3 |
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