{"title":"Relaxed area of 0-homogeneous maps in the strict BV-convergence","authors":"Simone Carano","doi":"10.1007/s10231-024-01435-1","DOIUrl":null,"url":null,"abstract":"<div><p>We compute the relaxed Cartesian area for a general 0-homogeneous map of bounded variation, with respect to the strict <i>BV</i>-convergence. In particular, we show that the relaxed area is finite for this class of maps and we provide an integral representation formula.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 5","pages":"2057 - 2074"},"PeriodicalIF":0.9000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01435-1","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 compute the relaxed Cartesian area for a general 0-homogeneous map of bounded variation, with respect to the strict BV-convergence. In particular, we show that the relaxed area is finite for this class of maps and we provide an integral representation formula.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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