{"title":"抛物型算子的类空间量化唯一性","authors":"Vedansh Arya, Agnid Banerjee","doi":"10.1016/j.matpur.2023.06.014","DOIUrl":null,"url":null,"abstract":"<div><p><span>We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a </span><span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> potential <em>V</em>. Our main result <span>Theorem 1.1</span> is a parabolic generalization of a well known result of Donnelly-Fefferman and Bakri. It also sharpens a previous result of Zhu that establishes similar vanishing order estimates which are instead averaged over time. The principal tool in our analysis is a new quantitative version of the well-known Escauriaza-Fernandez-Vessella type Carleman estimate that we establish in our setting.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Space-like quantitative uniqueness for parabolic operators\",\"authors\":\"Vedansh Arya, Agnid Banerjee\",\"doi\":\"10.1016/j.matpur.2023.06.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a </span><span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> potential <em>V</em>. Our main result <span>Theorem 1.1</span> is a parabolic generalization of a well known result of Donnelly-Fefferman and Bakri. It also sharpens a previous result of Zhu that establishes similar vanishing order estimates which are instead averaged over time. The principal tool in our analysis is a new quantitative version of the well-known Escauriaza-Fernandez-Vessella type Carleman estimate that we establish in our setting.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782423000880\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782423000880","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Space-like quantitative uniqueness for parabolic operators
We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a potential V. Our main result Theorem 1.1 is a parabolic generalization of a well known result of Donnelly-Fefferman and Bakri. It also sharpens a previous result of Zhu that establishes similar vanishing order estimates which are instead averaged over time. The principal tool in our analysis is a new quantitative version of the well-known Escauriaza-Fernandez-Vessella type Carleman estimate that we establish in our setting.
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