{"title":"Second-order approximation of free-discontinuity problems with linear growth","authors":"Teresa Esposito","doi":"10.3233/ASY-181476","DOIUrl":null,"url":null,"abstract":"with g : [0,+∞) → [0,+∞) increasing and bounded. The approximating functionals are of AmbrosioTortorelli type and depend on the Hessian or on the Laplacian of the edge variable v which thus belongs to W (Ω). When the space dimension is equal to two and three v is then continuous and this improved regularity leads to a sequence of approximating functionals which are ready to be used for numerical simulations.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"5 1","pages":"21-52"},"PeriodicalIF":0.0000,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptot. Anal.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/ASY-181476","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
with g : [0,+∞) → [0,+∞) increasing and bounded. The approximating functionals are of AmbrosioTortorelli type and depend on the Hessian or on the Laplacian of the edge variable v which thus belongs to W (Ω). When the space dimension is equal to two and three v is then continuous and this improved regularity leads to a sequence of approximating functionals which are ready to be used for numerical simulations.
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