Variational stabilization of degenerate p-elasticae
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912295736573952 |
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| author | Miura, Tatsuya Yoshizawa, Kensuke |
| author_facet | Miura, Tatsuya Yoshizawa, Kensuke |
| contents | A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar $p$-elasticae. It was known that in the non-degenerate regime $p\in(1,2]$, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime $p\in(2,\infty)$ there emerge uncountably many local minimizers with diverging energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Variational stabilization of degenerate p-elasticae Miura, Tatsuya Yoshizawa, Kensuke Analysis of PDEs Differential Geometry 49Q10, 53A04, and 33E05 A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar $p$-elasticae. It was known that in the non-degenerate regime $p\in(1,2]$, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime $p\in(2,\infty)$ there emerge uncountably many local minimizers with diverging energy. |
| title | Variational stabilization of degenerate p-elasticae |
| topic | Analysis of PDEs Differential Geometry 49Q10, 53A04, and 33E05 |
| url | https://arxiv.org/abs/2310.07451 |