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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.15026 |
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| _version_ | 1866915120891822080 |
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| author | Ashbaugh, Mark Bucur, Dorin Laugesen, Richard S. Leylekian, Roméo |
| author_facet | Ashbaugh, Mark Bucur, Dorin Laugesen, Richard S. Leylekian, Roméo |
| contents | We prove a fourth order analogue of the Saint-Venant inequality: the mean deflection of a clamped plate under uniform transverse load is maximal for the ball, among plates of prescribed volume in any dimension of space. The method works in Euclidean space, hyperbolic space, and the sphere.
Similar results for clamped plates under small compression and for the compliance under non-uniform loads are proved to hold in two dimensional Euclidean space, with the higher dimensional and curved cases of those problems left open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourth order Saint-Venant inequalities: maximizing compliance and mean deflection among clamped plates Ashbaugh, Mark Bucur, Dorin Laugesen, Richard S. Leylekian, Roméo Analysis of PDEs 35J35 We prove a fourth order analogue of the Saint-Venant inequality: the mean deflection of a clamped plate under uniform transverse load is maximal for the ball, among plates of prescribed volume in any dimension of space. The method works in Euclidean space, hyperbolic space, and the sphere. Similar results for clamped plates under small compression and for the compliance under non-uniform loads are proved to hold in two dimensional Euclidean space, with the higher dimensional and curved cases of those problems left open. |
| title | Fourth order Saint-Venant inequalities: maximizing compliance and mean deflection among clamped plates |
| topic | Analysis of PDEs 35J35 |
| url | https://arxiv.org/abs/2501.15026 |