Connecting disclinations by ridges
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914882292547584 |
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| author | Gladbach, Peter Olbermann, Heiner |
| author_facet | Gladbach, Peter Olbermann, Heiner |
| contents | We consider a thin elastic sheet with a finite number of disclinations in a variational framework in the Föppl-von Kármán approximation. Under the non-physical assumption that the out-of-plane displacement is a convex function, we prove that minimizers display ridges between the disclinations. We prove the associated energy scaling law with upper and lower bounds that match up to logarithmic factors in the thickness of the sheet. One of the key estimates in the proof that we consider of independent interest is a generalization of the monotonicity property of the Monge-Ampère measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connecting disclinations by ridges Gladbach, Peter Olbermann, Heiner Analysis of PDEs 49Q10, 74K20 We consider a thin elastic sheet with a finite number of disclinations in a variational framework in the Föppl-von Kármán approximation. Under the non-physical assumption that the out-of-plane displacement is a convex function, we prove that minimizers display ridges between the disclinations. We prove the associated energy scaling law with upper and lower bounds that match up to logarithmic factors in the thickness of the sheet. One of the key estimates in the proof that we consider of independent interest is a generalization of the monotonicity property of the Monge-Ampère measure. |
| title | Connecting disclinations by ridges |
| topic | Analysis of PDEs 49Q10, 74K20 |
| url | https://arxiv.org/abs/2405.10097 |