The two-well problem in three dimensions
We study properties of generalized convex hulls of the set K = SO(3) ∪ SO(3)H with det H > 0. If K contains no rank-1 connection we show that the quasiconvex hull of K is trivial if H belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of K can be...
| Egile Nagusiak: | , , , |
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| Formatua: | Journal article |
| Hizkuntza: | English |
| Argitaratua: |
2000
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| _version_ | 1826268319658803200 |
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| author | Dolzmann, G Kirchheim, B Muller, S Sverak, V |
| author_facet | Dolzmann, G Kirchheim, B Muller, S Sverak, V |
| author_sort | Dolzmann, G |
| collection | OXFORD |
| description | We study properties of generalized convex hulls of the set K = SO(3) ∪ SO(3)H with det H > 0. If K contains no rank-1 connection we show that the quasiconvex hull of K is trivial if H belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of K can be nontrivial if H is sufficiently far from the identity, while the (functional) rank-1 convex hull is always trivial. If the second well is replaced by a point then the polyconvex hull is trivial provided that there are no rank-1 connections. |
| first_indexed | 2024-03-06T21:07:52Z |
| format | Journal article |
| id | oxford-uuid:3d1428c5-21e1-4c2e-aaf1-88d4d8b4f54f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:07:52Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:3d1428c5-21e1-4c2e-aaf1-88d4d8b4f54f2022-03-26T14:17:26ZThe two-well problem in three dimensionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3d1428c5-21e1-4c2e-aaf1-88d4d8b4f54fEnglishSymplectic Elements at Oxford2000Dolzmann, GKirchheim, BMuller, SSverak, VWe study properties of generalized convex hulls of the set K = SO(3) ∪ SO(3)H with det H > 0. If K contains no rank-1 connection we show that the quasiconvex hull of K is trivial if H belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of K can be nontrivial if H is sufficiently far from the identity, while the (functional) rank-1 convex hull is always trivial. If the second well is replaced by a point then the polyconvex hull is trivial provided that there are no rank-1 connections. |
| spellingShingle | Dolzmann, G Kirchheim, B Muller, S Sverak, V The two-well problem in three dimensions |
| title | The two-well problem in three dimensions |
| title_full | The two-well problem in three dimensions |
| title_fullStr | The two-well problem in three dimensions |
| title_full_unstemmed | The two-well problem in three dimensions |
| title_short | The two-well problem in three dimensions |
| title_sort | two well problem in three dimensions |
| work_keys_str_mv | AT dolzmanng thetwowellprobleminthreedimensions AT kirchheimb thetwowellprobleminthreedimensions AT mullers thetwowellprobleminthreedimensions AT sverakv thetwowellprobleminthreedimensions AT dolzmanng twowellprobleminthreedimensions AT kirchheimb twowellprobleminthreedimensions AT mullers twowellprobleminthreedimensions AT sverakv twowellprobleminthreedimensions |