Unique continuation for the heat operator with potentials in weak spaces

We prove the strong unique continuation property for the differential inequalitywith V 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.d/2 loc , d ≥ 3. Their result was extended by

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Publication Details

Journal
Analysis & PDE
Published
2024-08-21
DOI
https://doi.org/10.2140/apde.2024.17.2257
Primary Topic
Advanced Mathematical Physics Problems
Type
article
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article

Unique continuation for the heat operator with potentials in weak spaces

Jaehyeon Ryu, Sanghyuk Lee, Eun-Hee Jeong
Analysis & PDE
Advanced Mathematical Physics Problems
article

Unique continuation for the heat operator with potentials in weak spaces

Jaehyeon Ryu, Sanghyuk Lee, Eun-Hee Jeong
article en

Abstract

We prove the strong unique continuation property for the differential inequalitywith V 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.d/2 loc , d ≥ 3. Their result was extended by

Analysis & PDEVol. 17(7)
Korea Institute for Advanced Study (KR), Seoul National University (KR), Jeonju National University of Education (KR), National Institute for Mathematical Sciences (KR), Jeonbuk National University (KR)
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Advanced Mathematical Physics Problems
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Unique continuation for the heat operator with potentials in weak spaces — Jaehyeon Ryu, Sanghyuk Lee, et al. · Analysis & PDE (2024) | TGRS Research Map | TGRS