Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions
The three-well problem consists in looking for minimizers u : Ω ⊂ R3 → R3 of a functional I (u) = ∫Ω W (∇ u) d x, where the elastic energy W models the tetragonal phase of a phase-transforming material. In particular, W attains its minimum on K = {n-ary union}i = 13 SO (3) Ui, with Ui being the thre...
| Hoofdauteurs: | , , |
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| Formaat: | Journal article |
| Taal: | English |
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2007
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| _version_ | 1826284687976300544 |
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| author | Conti, S Dolzmann, G Kirchheim, B |
| author_facet | Conti, S Dolzmann, G Kirchheim, B |
| author_sort | Conti, S |
| collection | OXFORD |
| description | The three-well problem consists in looking for minimizers u : Ω ⊂ R3 → R3 of a functional I (u) = ∫Ω W (∇ u) d x, where the elastic energy W models the tetragonal phase of a phase-transforming material. In particular, W attains its minimum on K = {n-ary union}i = 13 SO (3) Ui, with Ui being the three distinct diagonal matrices with eigenvalues (λ, λ, over(λ, ̃)), λ, over(λ, ̃) > 0 and λ ≠ over(λ, ̃). We show that, for boundary values F in a suitable relatively open subset of M3 × 3 ∩ {F : det F = det U1}, the differential inclusion{(∇ u ∈ K, in Ω,; u (x) = F x, on ∂ Ω) has Lipschitz solutions. © 2006 Elsevier Masson SAS. All rights reserved. |
| first_indexed | 2024-03-07T01:17:36Z |
| format | Journal article |
| id | oxford-uuid:8f3afc5c-1b4d-4a92-b793-0c92092d9d15 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:17:36Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:8f3afc5c-1b4d-4a92-b793-0c92092d9d152022-03-26T23:02:55ZExistence of Lipschitz minimizers for the three-well problem in solid-solid phase transitionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8f3afc5c-1b4d-4a92-b793-0c92092d9d15EnglishSymplectic Elements at Oxford2007Conti, SDolzmann, GKirchheim, BThe three-well problem consists in looking for minimizers u : Ω ⊂ R3 → R3 of a functional I (u) = ∫Ω W (∇ u) d x, where the elastic energy W models the tetragonal phase of a phase-transforming material. In particular, W attains its minimum on K = {n-ary union}i = 13 SO (3) Ui, with Ui being the three distinct diagonal matrices with eigenvalues (λ, λ, over(λ, ̃)), λ, over(λ, ̃) > 0 and λ ≠ over(λ, ̃). We show that, for boundary values F in a suitable relatively open subset of M3 × 3 ∩ {F : det F = det U1}, the differential inclusion{(∇ u ∈ K, in Ω,; u (x) = F x, on ∂ Ω) has Lipschitz solutions. © 2006 Elsevier Masson SAS. All rights reserved. |
| spellingShingle | Conti, S Dolzmann, G Kirchheim, B Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions |
| title | Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions |
| title_full | Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions |
| title_fullStr | Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions |
| title_full_unstemmed | Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions |
| title_short | Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions |
| title_sort | existence of lipschitz minimizers for the three well problem in solid solid phase transitions |
| work_keys_str_mv | AT contis existenceoflipschitzminimizersforthethreewellprobleminsolidsolidphasetransitions AT dolzmanng existenceoflipschitzminimizersforthethreewellprobleminsolidsolidphasetransitions AT kirchheimb existenceoflipschitzminimizersforthethreewellprobleminsolidsolidphasetransitions |