lions型引理的一个推广版本

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2023-08-28 DOI:10.2478/amsil-2023-0014

M. Chmara

{"title":"lions型引理的一个推广版本","authors":"M. Chmara","doi":"10.2478/amsil-2023-0014","DOIUrl":null,"url":null,"abstract":"Abstract In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space.","PeriodicalId":52359,"journal":{"name":"Annales Mathematicae Silesianae","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Generalized Version of the Lions-Type Lemma\",\"authors\":\"M. Chmara\",\"doi\":\"10.2478/amsil-2023-0014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space.\",\"PeriodicalId\":52359,\"journal\":{\"name\":\"Annales Mathematicae Silesianae\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematicae Silesianae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/amsil-2023-0014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae Silesianae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/amsil-2023-0014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要在这篇短文中，我回顾了在无界域的情况下处理序列缺乏紧致性的历史，并证明了Lebesgue可测函数序列的消失Lions型结果。这个引理推广了一类Orlicz–Sobolev空间的一些结果。这里重要的是积分的行为，而不是空间。

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

A Generalized Version of the Lions-Type Lemma

Abstract In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space.

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

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks