一般非局部线性椭圆和抛物问题的对称性结果

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-07-24 DOI:10.1016/j.matpur.2024.103597

Vincenzo Ferone , Gianpaolo Piscitelli , Bruno Volzone

{"title":"一般非局部线性椭圆和抛物问题的对称性结果","authors":"Vincenzo Ferone , Gianpaolo Piscitelli , Bruno Volzone","doi":"10.1016/j.matpur.2024.103597","DOIUrl":null,"url":null,"abstract":"<div>We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions.In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in [20].Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems.</div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"190 ","pages":"Article 103597"},"PeriodicalIF":2.1000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000953/pdfft?md5=19d057b2f02f47e1513406b709fa9d89&pid=1-s2.0-S0021782424000953-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Symmetrization results for general nonlocal linear elliptic and parabolic problems\",\"authors\":\"Vincenzo Ferone , Gianpaolo Piscitelli , Bruno Volzone\",\"doi\":\"10.1016/j.matpur.2024.103597\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions.In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in [20].Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems.</div>\",\"PeriodicalId\":51071,\"journal\":{\"name\":\"Journal de Mathematiques Pures et Appliquees\",\"volume\":\"190 \",\"pages\":\"Article 103597\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000953/pdfft?md5=19d057b2f02f47e1513406b709fa9d89&pid=1-s2.0-S0021782424000953-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal de Mathematiques Pures et Appliquees\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000953\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de Mathematiques Pures et Appliquees","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000953","RegionNum":1,"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

摘要

对于具有同质 Dirichlet 边界条件的一般非局部线性椭圆问题，我们以质量集中（积分比较）的形式建立了 Talenti 型对称性结果。

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

Symmetrization results for general nonlocal linear elliptic and parabolic problems

We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions.

In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in [20].

Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems.

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

Journal de Mathematiques Pures et Appliquees 数学-数学

CiteScore

4.30

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.