论圆柱体中的兰迪斯猜想

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI:10.1134/S1061920824040058

N.D. Filonov, S.T. Krymskii

{"title":"论圆柱体中的兰迪斯猜想","authors":"N.D. Filonov, S.T. Krymskii","doi":"10.1134/S1061920824040058","DOIUrl":null,"url":null,"abstract":" The equation \\(- \\Delta u + V u = 0\\) in the cylinder \\(\\mathbb{R} \\times (0,2\\pi)^d\\) with periodic boundary conditions is considered. The potential \\(V\\) is assumed to be bounded, and both functions \\(u\\) and \\(V\\) are assumed to be real-valued. It is shown that the fastest rate of decay at infinity of nontrivial solution \\(u\\) is \\(O\\left(e^{-c|w|}\\right)\\) for \\(d=1\\) or \\(2\\), and \\(O\\left(e^{-c|w|^{4/3}}\\right)\\) for \\(d\\ge 3\\). Here \\(w\\) stands for the axial variable. DOI 10.1134/S1061920824040058 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"645 - 665"},"PeriodicalIF":1.7000,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Landis Conjecture in a Cylinder\",\"authors\":\"N.D. Filonov, S.T. Krymskii\",\"doi\":\"10.1134/S1061920824040058\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" The equation \\\\(- \\\\Delta u + V u = 0\\\\) in the cylinder \\\\(\\\\mathbb{R} \\\\times (0,2\\\\pi)^d\\\\) with periodic boundary conditions is considered. The potential \\\\(V\\\\) is assumed to be bounded, and both functions \\\\(u\\\\) and \\\\(V\\\\) are assumed to be real-valued. It is shown that the fastest rate of decay at infinity of nontrivial solution \\\\(u\\\\) is \\\\(O\\\\left(e^{-c|w|}\\\\right)\\\\) for \\\\(d=1\\\\) or \\\\(2\\\\), and \\\\(O\\\\left(e^{-c|w|^{4/3}}\\\\right)\\\\) for \\\\(d\\\\ge 3\\\\). Here \\\\(w\\\\) stands for the axial variable. DOI 10.1134/S1061920824040058 \",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"31 4\",\"pages\":\"645 - 665\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920824040058\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824040058","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

考虑具有周期边界条件的圆柱体\(\mathbb{R} \times (0,2\pi)^d\)中的方程\(- \Delta u + V u = 0\)。假设势能\(V\)是有界的，假设函数\(u\)和\(V\)都是实值。结果表明，对于\(d=1\)或\(2\)，非平凡解\(u\)在无穷远处的衰减速度最快为\(O\left(e^{-c|w|}\right)\)，对于\(d\ge 3\)，衰减速度最快为\(O\left(e^{-c|w|^{4/3}}\right)\)。这里\(w\)代表轴向变量。Doi 10.1134/ s1061920824040058

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

On the Landis Conjecture in a Cylinder

The equation \(- \Delta u + V u = 0\) in the cylinder \(\mathbb{R} \times (0,2\pi)^d\) with periodic boundary conditions is considered. The potential \(V\) is assumed to be bounded, and both functions \(u\) and \(V\) are assumed to be real-valued. It is shown that the fastest rate of decay at infinity of nontrivial solution \(u\) is \(O\left(e^{-c|w|}\right)\) for \(d=1\) or \(2\), and \(O\left(e^{-c|w|^{4/3}}\right)\) for \(d\ge 3\). Here \(w\) stands for the axial variable.

DOI 10.1134/S1061920824040058

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

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.