{"title":"Steklov特征函数的下界","authors":"Jeffrey Galkowski, John A. Toth","doi":"10.4310/pamq.2023.v19.n4.a7","DOIUrl":null,"url":null,"abstract":"Let $(\\Omega,g)$ be a compact, real analytic Riemannian manifold with real analytic boundary $\\partial \\Omega = M$. We give $L^2$-lower bounds for Steklov eigenfunctions and their restrictions to interior hypersurfaces $H \\subset \\Omega^\\circ$ in a geometrically defined neighborhood of $M$. Our results are optimal in the entire geometric neighborhood and complement the results on eigenfunction upper bounds in $\\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=3897008}{[\\textrm{GT19}]}$","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"195 2","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":"{\"title\":\"Lower bounds for Steklov eigenfunctions\",\"authors\":\"Jeffrey Galkowski, John A. Toth\",\"doi\":\"10.4310/pamq.2023.v19.n4.a7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $(\\\\Omega,g)$ be a compact, real analytic Riemannian manifold with real analytic boundary $\\\\partial \\\\Omega = M$. We give $L^2$-lower bounds for Steklov eigenfunctions and their restrictions to interior hypersurfaces $H \\\\subset \\\\Omega^\\\\circ$ in a geometrically defined neighborhood of $M$. Our results are optimal in the entire geometric neighborhood and complement the results on eigenfunction upper bounds in $\\\\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=3897008}{[\\\\textrm{GT19}]}$\",\"PeriodicalId\":54526,\"journal\":{\"name\":\"Pure and Applied Mathematics Quarterly\",\"volume\":\"195 2\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"28\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Mathematics Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2023.v19.n4.a7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2023.v19.n4.a7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let $(\Omega,g)$ be a compact, real analytic Riemannian manifold with real analytic boundary $\partial \Omega = M$. We give $L^2$-lower bounds for Steklov eigenfunctions and their restrictions to interior hypersurfaces $H \subset \Omega^\circ$ in a geometrically defined neighborhood of $M$. Our results are optimal in the entire geometric neighborhood and complement the results on eigenfunction upper bounds in $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=3897008}{[\textrm{GT19}]}$
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