一类麦克斯韦-薛定谔系统的正则效应

IF 1.3 2区 数学 Q1 MATHEMATICS
Ayana Pinheiro de Castro Santana , Luís Henrique de Miranda
{"title":"一类麦克斯韦-薛定谔系统的正则效应","authors":"Ayana Pinheiro de Castro Santana ,&nbsp;Luís Henrique de Miranda","doi":"10.1016/j.na.2024.113625","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we prove existence and regularity of weak solutions for the following system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mtext>div</mtext><mrow><mo>(</mo><mi>M</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mspace></mspace></mtd></mtr><mtr><mtd><mo>−</mo><mtext>div</mtext><mrow><mo>(</mo><mi>M</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mspace></mspace></mtd></mtr><mtr><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>u</mi><mo>=</mo><mi>v</mi><mo>=</mo><mn>0</mn><mspace></mspace><mspace></mspace><mtext>on</mtext><mspace></mspace><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mi>Ω</mi></math></span> is an open bounded subset of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, for <span><math><mrow><mi>N</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mi>M</mi></math></span> is a matrix with Lipschitz coefficients, <span><math><mrow><mi>m</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mi>g</mi></math></span>, <span><math><mi>h</mi></math></span> are two Carathéodory functions. We prove that under appropriate conditions on <span><math><mi>g</mi></math></span> and <span><math><mi>h</mi></math></span>, there exist solutions which escape the predicted regularity by the classical Stampacchia’s theory causing the so-called regularizing effect.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"248 ","pages":"Article 113625"},"PeriodicalIF":1.3000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularizing effect for a class of Maxwell–Schrödinger systems\",\"authors\":\"Ayana Pinheiro de Castro Santana ,&nbsp;Luís Henrique de Miranda\",\"doi\":\"10.1016/j.na.2024.113625\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we prove existence and regularity of weak solutions for the following system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mtext>div</mtext><mrow><mo>(</mo><mi>M</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mspace></mspace></mtd></mtr><mtr><mtd><mo>−</mo><mtext>div</mtext><mrow><mo>(</mo><mi>M</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mspace></mspace></mtd></mtr><mtr><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>u</mi><mo>=</mo><mi>v</mi><mo>=</mo><mn>0</mn><mspace></mspace><mspace></mspace><mtext>on</mtext><mspace></mspace><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mi>Ω</mi></math></span> is an open bounded subset of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, for <span><math><mrow><mi>N</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mi>M</mi></math></span> is a matrix with Lipschitz coefficients, <span><math><mrow><mi>m</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mi>g</mi></math></span>, <span><math><mi>h</mi></math></span> are two Carathéodory functions. We prove that under appropriate conditions on <span><math><mi>g</mi></math></span> and <span><math><mi>h</mi></math></span>, there exist solutions which escape the predicted regularity by the classical Stampacchia’s theory causing the so-called regularizing effect.</p></div>\",\"PeriodicalId\":49749,\"journal\":{\"name\":\"Nonlinear Analysis-Theory Methods & Applications\",\"volume\":\"248 \",\"pages\":\"Article 113625\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Theory Methods & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0362546X24001445\",\"RegionNum\":2,\"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":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24001445","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

摘要

本文证明了以下系统弱解的存在性和正则性-div(M(x)∇u)+g(x,u,v)=finΩ-div(M(x)∇v)=h(x,u,v)inΩu=v=0on∂Ω,其中Ω是 RN 的开放有界子集,对于 N>;2,f∈Lm(Ω),M 是具有 Lipschitz 系数的矩阵,m>1 和 g, h 是两个 Carathéodory 函数。我们证明,在 g 和 h 的适当条件下,存在一些解,它们摆脱了经典的斯坦帕奇亚理论所预测的正则性,从而产生了所谓的正则化效应。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Regularizing effect for a class of Maxwell–Schrödinger systems

In this paper we prove existence and regularity of weak solutions for the following system div(M(x)u)+g(x,u,v)=finΩdiv(M(x)v)=h(x,u,v)inΩu=v=0onΩ,where Ω is an open bounded subset of RN, for N>2, fLm(Ω), M is a matrix with Lipschitz coefficients, m>1 and g, h are two Carathéodory functions. We prove that under appropriate conditions on g and h, there exist solutions which escape the predicted regularity by the classical Stampacchia’s theory causing the so-called regularizing effect.

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
CiteScore
3.30
自引率
0.00%
发文量
265
审稿时长
60 days
期刊介绍: Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信