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arXiv · 2203.08535

Complete classification of planar p-elasticae

Tatsuya Miura·Kensuke Yoshizawa
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Abstract

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.

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Tatsuya Miura, Kensuke Yoshizawa. 2022-03-16. Complete classification of planar p-elasticae. https://doi.org/10.1007/s10231-024-01445-z

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