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Unique continuation
for the heat operator with potentials in weak spaces
Eunhee Jeong, Sanghyuk Lee and Jaehyeon Ryu |
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Vol. 17 (2024), No. 7, 2257–2274
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Abstract |
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We prove the strong unique continuation property for the differential inequality with contained in weak spaces. In particular, we establish the strong unique continuation property for , which has been left open since the works of Escauriaza (2000) and Escauriaza and Vega (2001). Our results are consequences of the Carleman estimates for the heat operator in the Lorentz spaces. |
Keywords
unique continuation, the heat equation, Carleman estimate,
Hermite operator
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Mathematical Subject Classification
Primary: 35K05
Secondary: 35B60
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Milestones
Received: 23 September 2021
Revised: 25 July 2022
Accepted: 7 March 2023
Published: 21 August 2024
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Authors |
| Eunhee Jeong | |
| Department of Mathematics Education,
and Institute of Pure and Applied Mathematics Jeonbuk National University Jeonju South Korea |
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| Sanghyuk Lee | |
| Department of Mathematical Sciences
and RIM Seoul National University Seoul South Korea |
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| Jaehyeon Ryu | |
| School of Mathematics Korea Institute for Advanced Study Seoul South Korea |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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