Wrinkling in the Lamé problem: a $Γ$-convergence approach
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913146152681472 |
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| author | Marziani, Roberta |
| author_facet | Marziani, Roberta |
| contents | We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the Föppl--von Kármán theory. Building on the analysis of the Lamé problem in Bella and Kohn, we investigate the asymptotic regime $h\to0$ and establish a $Γ$-convergence result for suitably rescaled energies after subtraction of the relaxed membrane energy. The limiting functional is a scalar convex measure-valued energy coupled with a constraint on the marginal of the limiting measure, describing the distribution of wrinkle frequencies. We also prove existence and qualitative properties of minimizers of the limiting functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wrinkling in the Lamé problem: a $Γ$-convergence approach Marziani, Roberta Analysis of PDEs 35B27, 49J45, 74K25, 49S05 We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the Föppl--von Kármán theory. Building on the analysis of the Lamé problem in Bella and Kohn, we investigate the asymptotic regime $h\to0$ and establish a $Γ$-convergence result for suitably rescaled energies after subtraction of the relaxed membrane energy. The limiting functional is a scalar convex measure-valued energy coupled with a constraint on the marginal of the limiting measure, describing the distribution of wrinkle frequencies. We also prove existence and qualitative properties of minimizers of the limiting functional. |
| title | Wrinkling in the Lamé problem: a $Γ$-convergence approach |
| topic | Analysis of PDEs 35B27, 49J45, 74K25, 49S05 |
| url | https://arxiv.org/abs/2605.19598 |