{"title":"Discrete approximation of nonlocal-gradient energies","authors":"Andrea Braides, Andrea Causin, Margherita Solci","doi":"10.1515/acv-2023-0028","DOIUrl":null,"url":null,"abstract":"We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces. The key ingredient in the proof is a formulation in terms of circulant Toeplitz matrices.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":"23 16","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/acv-2023-0028","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces. The key ingredient in the proof is a formulation in terms of circulant Toeplitz matrices.
期刊介绍：
Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.
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