Complete classification of planar p-elasticae
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913539517579264 |
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| author | Miura, Tatsuya Yoshizawa, Kensuke |
| author_facet | Miura, Tatsuya Yoshizawa, Kensuke |
| contents | Euler's elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its $L^p$-counterpart is called $p$-elastica. In this paper we completely classify all $p$-elasticae in the plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new types of $p$-elliptic functions which streamline the whole argument and result. As an application we also classify all closed planar $p$-elasticae. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_08535 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Complete classification of planar p-elasticae Miura, Tatsuya Yoshizawa, Kensuke Analysis of PDEs Classical Analysis and ODEs Differential Geometry 49Q10, 53A04, and 33E05 Euler's elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its $L^p$-counterpart is called $p$-elastica. In this paper we completely classify all $p$-elasticae in the plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new types of $p$-elliptic functions which streamline the whole argument and result. As an application we also classify all closed planar $p$-elasticae. |
| title | Complete classification of planar p-elasticae |
| topic | Analysis of PDEs Classical Analysis and ODEs Differential Geometry 49Q10, 53A04, and 33E05 |
| url | https://arxiv.org/abs/2203.08535 |