{"title":"Quantitative uniqueness of solutions to a class of Schrödinger equations with inverse square potentials","authors":"Xiujin Chen , Hairong Liu","doi":"10.1016/j.jmaa.2024.129032","DOIUrl":null,"url":null,"abstract":"<div><div>This paper is devoted to proving the quantitative unique continuation property for solutions to a class of Schrödinger equations with inverse square potentials. The argument is to introduce a frequency function and show an almost monotonicity formula and three-ball inequalities by combining the Hardy's inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129032"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009545","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
Abstract
This paper is devoted to proving the quantitative unique continuation property for solutions to a class of Schrödinger equations with inverse square potentials. The argument is to introduce a frequency function and show an almost monotonicity formula and three-ball inequalities by combining the Hardy's inequality.
期刊介绍：
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.
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