Pinned planar p-elasticae
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909555469844480 |
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| author | Miura, Tatsuya Yoshizawa, Kensuke |
| author_facet | Miura, Tatsuya Yoshizawa, Kensuke |
| contents | Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p \simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic networks, extending a recent result of Dall'Acqua--Novaga--Pluda. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05721 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pinned planar p-elasticae Miura, Tatsuya Yoshizawa, Kensuke Differential Geometry Analysis of PDEs 49Q10, 53A04, 33E05 Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p \simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic networks, extending a recent result of Dall'Acqua--Novaga--Pluda. |
| title | Pinned planar p-elasticae |
| topic | Differential Geometry Analysis of PDEs 49Q10, 53A04, 33E05 |
| url | https://arxiv.org/abs/2209.05721 |