{"title":"The infinity-Laplacian in smooth convex domains and in a square","authors":"Karl K. Brustad, E. Lindgren, P. Lindqvist","doi":"10.3934/mine.2023080","DOIUrl":null,"url":null,"abstract":"<abstract><p>We extend some theorems for the infinity-ground state and for the infinity-potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent <italic>explicit</italic> solution disproves a conjecture.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mine.2023080","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 3
Abstract
We extend some theorems for the infinity-ground state and for the infinity-potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a conjecture.
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