{"title":"Revisited convexity notions for $$L^\\infty $$ variational problems","authors":"Ana Margarida Ribeiro, Elvira Zappale","doi":"10.1007/s13163-024-00499-0","DOIUrl":null,"url":null,"abstract":"<p>We address a detailed study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals, as well as those arising by the <span>\\(L^p\\)</span>-approximation, as <span>\\(p \\rightarrow +\\infty \\)</span> of such functionals. Our quest is motivated by the knowledge we have on the analogous integral functionals and aims at establishing a solid groundwork underlying further research in the <span>\\(L^\\infty \\)</span> context.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matemática Complutense","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13163-024-00499-0","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 address a detailed study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals, as well as those arising by the \(L^p\)-approximation, as \(p \rightarrow +\infty \) of such functionals. Our quest is motivated by the knowledge we have on the analogous integral functionals and aims at establishing a solid groundwork underlying further research in the \(L^\infty \) context.