临界边界情况下奇异漂移的拉普拉斯算子

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-11-27 DOI:10.1002/mana.202400098

D. Kinzebulatov

{"title":"临界边界情况下奇异漂移的拉普拉斯算子","authors":"D. Kinzebulatov","doi":"10.1002/mana.202400098","DOIUrl":null,"url":null,"abstract":"We establish well-posedness and regularity results for parabolic diffusion equation on the torus in the case when the singularities of a general drift reach the critical magnitude. The latter dictates the need to work in an Orlicz space situated between all <math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mi>p</mi>\n </msup>\n <annotation>$L^p$</annotation>\n </semantics></math> and <math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mi>∞</mi>\n </msup>\n <annotation>$L^\\infty$</annotation>\n </semantics></math>.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"511-526"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Laplacian with singular drift in a critical borderline case\",\"authors\":\"D. Kinzebulatov\",\"doi\":\"10.1002/mana.202400098\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish well-posedness and regularity results for parabolic diffusion equation on the torus in the case when the singularities of a general drift reach the critical magnitude. The latter dictates the need to work in an Orlicz space situated between all <math>\\n <semantics>\\n <msup>\\n <mi>L</mi>\\n <mi>p</mi>\\n </msup>\\n <annotation>$L^p$</annotation>\\n </semantics></math> and <math>\\n <semantics>\\n <msup>\\n <mi>L</mi>\\n <mi>∞</mi>\\n </msup>\\n <annotation>$L^\\\\infty$</annotation>\\n </semantics></math>.\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"298 2\",\"pages\":\"511-526\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400098\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400098","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在一般漂移奇点达到临界量级的情况下，建立了抛物扩散方程在环面上的适定性和正则性结果。后者决定了需要在位于所有L p $L^p$和L∞$L^\infty$之间的Orlicz空间中工作。

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

Laplacian with singular drift in a critical borderline case

We establish well-posedness and regularity results for parabolic diffusion equation on the torus in the case when the singularities of a general drift reach the critical magnitude. The latter dictates the need to work in an Orlicz space situated between all $L^{p}$ and $L^{\infty}$ .

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index