{"title":"用分段二次同胚和微分同胚逼近平面Sobolev w2,1同胚","authors":"D. Campbell, S. Hencl","doi":"10.1051/COCV/2021019","DOIUrl":null,"url":null,"abstract":"Given a Sobolev homeomorphism $f\\in W^{2,1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $\\epsilon$ measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the $W^{2,1}$ norm on this set.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms\",\"authors\":\"D. Campbell, S. Hencl\",\"doi\":\"10.1051/COCV/2021019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a Sobolev homeomorphism $f\\\\in W^{2,1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $\\\\epsilon$ measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the $W^{2,1}$ norm on this set.\",\"PeriodicalId\":8426,\"journal\":{\"name\":\"arXiv: Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/COCV/2021019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/COCV/2021019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms
Given a Sobolev homeomorphism $f\in W^{2,1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $\epsilon$ measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the $W^{2,1}$ norm on this set.
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