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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.06401 |
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| _version_ | 1866909598150033408 |
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| author | Albin, Nathan Nesi, Vincenzo Palombaro, Mariapia |
| author_facet | Albin, Nathan Nesi, Vincenzo Palombaro, Mariapia |
| contents | We study the differential inclusion $Du\in K$, where $K$ is an unbounded and rotationally invariant subset of the real symmetric $3\times 3$ matrices. We exhibit a subset of all possible average fields. The corresponding microgeometries are laminates of infinite rank. The problem originated in the search for the effective conductivity of polycrystalline composites. In the latter context, our result is an improvement of the previously known bounds established by Nesi $\&$ Milton, hence proving the optimality of a new full-measure class of microgeometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential inclusions and polycrystals Albin, Nathan Nesi, Vincenzo Palombaro, Mariapia Analysis of PDEs 35B27, 49J45 We study the differential inclusion $Du\in K$, where $K$ is an unbounded and rotationally invariant subset of the real symmetric $3\times 3$ matrices. We exhibit a subset of all possible average fields. The corresponding microgeometries are laminates of infinite rank. The problem originated in the search for the effective conductivity of polycrystalline composites. In the latter context, our result is an improvement of the previously known bounds established by Nesi $\&$ Milton, hence proving the optimality of a new full-measure class of microgeometries. |
| title | Differential inclusions and polycrystals |
| topic | Analysis of PDEs 35B27, 49J45 |
| url | https://arxiv.org/abs/2402.06401 |