具有幂权的分数Sobolev空间

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2021-10-08 DOI:10.2422/2036-2145.202112_002

Michał Kijaczko

{"title":"具有幂权的分数Sobolev空间","authors":"Michał Kijaczko","doi":"10.2422/2036-2145.202112_002","DOIUrl":null,"url":null,"abstract":". We investigate the form of the closure of the smooth, compactly supported functions C ∞ c (Ω) in the weighted fractional Sobolev space W s,p ; w,v (Ω) for bounded Ω . We focus on the weights w, v being powers of the distance to the boundary of the domain. Our results depend on the lower and upper Assouad codimension of the boundary of Ω . For such weights we also prove the comparability between the full weighted fractional Gagliardo seminorm and the truncated one.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"89 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Fractional Sobolev spaces with power weights\",\"authors\":\"Michał Kijaczko\",\"doi\":\"10.2422/2036-2145.202112_002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We investigate the form of the closure of the smooth, compactly supported functions C ∞ c (Ω) in the weighted fractional Sobolev space W s,p ; w,v (Ω) for bounded Ω . We focus on the weights w, v being powers of the distance to the boundary of the domain. Our results depend on the lower and upper Assouad codimension of the boundary of Ω . For such weights we also prove the comparability between the full weighted fractional Gagliardo seminorm and the truncated one.\",\"PeriodicalId\":8132,\"journal\":{\"name\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"volume\":\"89 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2422/2036-2145.202112_002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2422/2036-2145.202112_002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 5

摘要

．研究了加权分数Sobolev空间中光滑紧支撑函数C∞C (Ω)的闭包形式;W v (Ω)对于有界的Ω。我们关注权重w, v是到定义域边界距离的幂。我们的结果依赖于Ω边界的上下协维。对于这些权值，我们还证明了满权分数型Gagliardo半模与截断半模的可比性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Fractional Sobolev spaces with power weights

. We investigate the form of the closure of the smooth, compactly supported functions C ∞ c (Ω) in the weighted fractional Sobolev space W s,p ; w,v (Ω) for bounded Ω . We focus on the weights w, v being powers of the distance to the boundary of the domain. Our results depend on the lower and upper Assouad codimension of the boundary of Ω . For such weights we also prove the comparability between the full weighted fractional Gagliardo seminorm and the truncated one.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

自引率

0.00%

发文量