{"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":"210 ","pages":""},"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}
引用次数: 1
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.
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