{"title":"平行四边形和恒宽域的最低诺依曼特征值估计值","authors":"Corentin Léna, Jonathan Rohleder","doi":"10.1007/s13324-024-00900-7","DOIUrl":null,"url":null,"abstract":"<div><p>We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 3","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00900-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width\",\"authors\":\"Corentin Léna, Jonathan Rohleder\",\"doi\":\"10.1007/s13324-024-00900-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.</p></div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"14 3\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s13324-024-00900-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13324-024-00900-7\",\"RegionNum\":3,\"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":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00900-7","RegionNum":3,"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
我们证明了两类域中 Neumann Laplacian 的第一和第二非难特征值的尖锐上限：平行四边形和恒宽域。这特别给出了 A. Henrot、A. Lemenant 和 I. Lucardesi 最近获得的平行四边形等周不等式的新证明。
Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width
We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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