Francesco Boarotto, Roberto Monti, Alessandro Socionovo
{"title":"Higher Order Goh Conditions for Singular Extremals of Corank 1","authors":"Francesco Boarotto, Roberto Monti, Alessandro Socionovo","doi":"10.1007/s00205-024-01964-2","DOIUrl":null,"url":null,"abstract":"<div><p>We prove Goh conditions of order <span>\\(n\\geqq 3\\)</span> for strictly singular length-minimizing curves of corank 1, under the assumption that the domain of the <i>n</i>th instrinsic differential is of finite codimension. This result relies upon the proof of an open mapping theorem for maps with a regular <i>n</i>th differential.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"248 2","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-024-01964-2","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We prove Goh conditions of order \(n\geqq 3\) for strictly singular length-minimizing curves of corank 1, under the assumption that the domain of the nth instrinsic differential is of finite codimension. This result relies upon the proof of an open mapping theorem for maps with a regular nth differential.
期刊介绍：
The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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