{"title":"平面 p-elasticae 的完整分类","authors":"Tatsuya Miura, Kensuke Yoshizawa","doi":"10.1007/s10231-024-01445-z","DOIUrl":null,"url":null,"abstract":"<p>Euler’s elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its <span>\\(L^p\\)</span>-counterpart is called <i>p</i>-elastica. In this paper we completely classify all <i>p</i>-elasticae in the plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new types of <i>p</i>-elliptic functions which streamline the whole argument and result. As an application we also classify all closed planar <i>p</i>-elasticae.\n</p>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complete classification of planar p-elasticae\",\"authors\":\"Tatsuya Miura, Kensuke Yoshizawa\",\"doi\":\"10.1007/s10231-024-01445-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Euler’s elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its <span>\\\\(L^p\\\\)</span>-counterpart is called <i>p</i>-elastica. In this paper we completely classify all <i>p</i>-elasticae in the plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new types of <i>p</i>-elliptic functions which streamline the whole argument and result. As an application we also classify all closed planar <i>p</i>-elasticae.\\n</p>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10231-024-01445-z\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10231-024-01445-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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