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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-024-01964-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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.