A compactness and structure result for a discrete multi-well problem with SO(n) symmetry in arbitrary dimension
In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the modelling of surface energies in certain phase transiti...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
22 Nov 2017
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| In: |
Arxiv
Year: 2017, Pages: 1-19 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1711.08271
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| Author Notes: | Georgy Kitavtsev, Gianluca Lauteri, Stephan Luckhaus, and Angkana Rüland |
| Summary: | In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the modelling of surface energies in certain phase transitions. Mathematically, a main novelty here is the reduction of the problem to an incompatible one-well problem. The presented argument is very robust and applies to a number of different physically interesting models, including for instance phase transformations in shape-memory materials but also anti-ferromagnetic transformations or related transitions with an "internal" microstructure on smaller scales. |
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| Item Description: | Gesehen am 19.05.2021 |
| Physical Description: | Online Resource |