{"title":"Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies","authors":"Patricia Alonso Ruiz, Fabrice Baudoin","doi":"10.2422/2036-2145.202302_013","DOIUrl":null,"url":null,"abstract":"This paper establishes sufficient general conditions for the existence of Mosco limits of Korevaar-Schoen $L^2$ energies, first in the context of Cheeger spaces and then in the context of fractal-like spaces with walk dimension greater than 2. Among the ingredients, a new Rellich-Kondrachov type theorem for Korevaar-Schoen-Sobolev spaces is of independent interest.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2422/2036-2145.202302_013","RegionNum":2,"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
This paper establishes sufficient general conditions for the existence of Mosco limits of Korevaar-Schoen $L^2$ energies, first in the context of Cheeger spaces and then in the context of fractal-like spaces with walk dimension greater than 2. Among the ingredients, a new Rellich-Kondrachov type theorem for Korevaar-Schoen-Sobolev spaces is of independent interest.
期刊介绍:
The Annals of the Normale Superiore di Pisa, Science Class, publishes papers that contribute to the development of Mathematics both from the theoretical and the applied point of view. Research papers or papers of expository type are considered for publication.
The Annals of the Normale Scuola di Pisa - Science Class is published quarterly
Soft cover, 17x24