弱空间中具有势的热算子的唯一延续

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-21 DOI:10.2140/apde.2024.17.2257

Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu

引用次数: 0

摘要

我们证明了微分不等式 |(∂t+ Δ)u(x,t)|≤V(x,t)|u(x,t)| 的强唯一连续性，其中 V 包含在弱空间中。特别是，我们建立了 V∈ Lt∞Lx[t]d∕2,∞ 的强唯一延续性质，这是自 Escauriaza (2000) 和 Escauriaza and Vega (2001) 的著作以来一直悬而未决的问题。我们的结果是洛伦兹空间中热算子的卡勒曼估计的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Unique continuation for the heat operator with potentials in weak spaces

We prove the strong unique continuation property for the differential inequality

| (\partial_{t} + Δ) u (x, t) | \leq V (x, t) | u (x, t) |,

with $V$ contained in weak spaces. In particular, we establish the strong unique continuation property for $V \in L_{t}^{\infty} L_{x}^{[t] d ∕ 2, \infty}$ , 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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.