论文标题
平面P弹性的完整分类
Complete classification of planar p-elasticae
论文作者
论文摘要
Euler的Elastica由固定长度约束下总平方曲率的临界点定义，其$ l^p $ -counterPart称为$ p $ -Elastica。在本文中，我们将所有$ p $ - 弹性机完全分类为飞机，并获得其明确的公式以及最佳的规律性。为此，我们介绍了新型的$ p $ elliptic函数，这些功能简化了整个参数和结果。作为一个应用程序，我们还对所有封闭的平面$ p $ - 弹性机分类进行了分类。
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.
