{"title":"On Fractional Smoothness of Modulus of Functions","authors":"Dong Li","doi":"10.4208/aam.oa-2021-0006","DOIUrl":null,"url":null,"abstract":"We consider the Nemytskii operators $u\\to |u|$ and $u\\to u^{\\pm}$ in a bounded domain $\\Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(\\Omega)$ with $0\\le s<3/2$.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用数学年刊:英文版","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4208/aam.oa-2021-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the Nemytskii operators $u\to |u|$ and $u\to u^{\pm}$ in a bounded domain $\Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(\Omega)$ with $0\le s<3/2$.
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