{"title":"Structure of level sets and Sard-type properties of Lipschitz maps","authors":"G. Alberti, S. Bianchini, Gianluca Crippa","doi":"10.2422/2036-2145.201107_006","DOIUrl":null,"url":null,"abstract":"We consider certain properties of maps of class C 2 from R d to R d 1 that are strictly related to Sard's theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give examples showing that, in term of regularity, our results are optimal.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"26 1","pages":"863-902"},"PeriodicalIF":1.2000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"84","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2422/2036-2145.201107_006","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 84
Abstract
We consider certain properties of maps of class C 2 from R d to R d 1 that are strictly related to Sard's theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give examples showing that, in term of regularity, our results are optimal.
期刊介绍：
The Annals of the Normale Superiore di Pisa, Science Class, publishes papers that contribute to the development of Mathematics both from the theoretical and the applied point of view. Research papers or papers of expository type are considered for publication.
The Annals of the Normale Scuola di Pisa - Science Class is published quarterly
Soft cover, 17x24
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