Refined approximation for minimizers of a Landau-de Gennes energy functional
We study minimizers of a Landau-de Gennes energy functional in the asymptotic regime of small dimensionless elastic constant L > 0. The results on the convergence to a minimizer of the limit Oseen-Frank functional in Majumdar and Zarnescu (Arch Ration Mech Anal 196:227–280, 2010) are revisite...
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| Format: | Journal article |
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Springer
2012
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| _version_ | 1797065650692161536 |
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| author | Nguyen, L Zarnescu, A |
| author_facet | Nguyen, L Zarnescu, A |
| author_sort | Nguyen, L |
| collection | OXFORD |
| description | We study minimizers of a Landau-de Gennes energy functional in the asymptotic regime of small dimensionless elastic constant L > 0. The results on the convergence to a minimizer of the limit Oseen-Frank functional in Majumdar and Zarnescu (Arch Ration Mech Anal 196:227–280, 2010) are revisited and improved, which in effect lead to a sharp rate of convergence. The equation for the first-order correction term is derived: it has a “normal component” given by an algebraic relation and a “tangential component” given by a linear system. |
| first_indexed | 2024-03-06T21:31:37Z |
| format | Journal article |
| id | oxford-uuid:44de260b-4255-4644-8b0a-be791971095c |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:31:37Z |
| publishDate | 2012 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:44de260b-4255-4644-8b0a-be791971095c2022-03-26T15:04:18ZRefined approximation for minimizers of a Landau-de Gennes energy functionalJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:44de260b-4255-4644-8b0a-be791971095cSymplectic Elements at OxfordSpringer2012Nguyen, LZarnescu, AWe study minimizers of a Landau-de Gennes energy functional in the asymptotic regime of small dimensionless elastic constant L > 0. The results on the convergence to a minimizer of the limit Oseen-Frank functional in Majumdar and Zarnescu (Arch Ration Mech Anal 196:227–280, 2010) are revisited and improved, which in effect lead to a sharp rate of convergence. The equation for the first-order correction term is derived: it has a “normal component” given by an algebraic relation and a “tangential component” given by a linear system. |
| spellingShingle | Nguyen, L Zarnescu, A Refined approximation for minimizers of a Landau-de Gennes energy functional |
| title | Refined approximation for minimizers of a Landau-de Gennes energy functional |
| title_full | Refined approximation for minimizers of a Landau-de Gennes energy functional |
| title_fullStr | Refined approximation for minimizers of a Landau-de Gennes energy functional |
| title_full_unstemmed | Refined approximation for minimizers of a Landau-de Gennes energy functional |
| title_short | Refined approximation for minimizers of a Landau-de Gennes energy functional |
| title_sort | refined approximation for minimizers of a landau de gennes energy functional |
| work_keys_str_mv | AT nguyenl refinedapproximationforminimizersofalandaudegennesenergyfunctional AT zarnescua refinedapproximationforminimizersofalandaudegennesenergyfunctional |