UNIQUE CONTINUATION FOR THE HEAT OPERATOR WITH POTENTIALS IN WEAK SPACES

Eunhee Jeong; Sanghyuk Lee; Jaehyeon Ryu

doi:10.2140/apde.2024.17.2257

UNIQUE CONTINUATION FOR THE HEAT OPERATOR WITH POTENTIALS IN WEAK SPACES

Eunhee Jeong
, Sanghyuk Lee
, Jaehyeon Ryu

Department of Mathematics Education

Seoul National University
Korea Institute for Advanced Study

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

Abstract

We prove the strong unique continuation property for the differential inequality |(∂_t + Δ)u(x, t)| ≤ V(x, t)|u(x, t)|, with V contained in weak spaces. In particular, we establish the strong unique continuation property for V ∈ L^∞_tL^d/2,∞_x, 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.

Original language	English
Pages (from-to)	2257-2274
Number of pages	18
Journal	Analysis and PDE
Volume	17
Issue number	7
DOIs	https://doi.org/10.2140/apde.2024.17.2257
State	Published - 2024

Keywords

Carleman estimate
Hermite operator
the heat equation
unique continuation

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.2140/apde.2024.17.2257

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title = "UNIQUE CONTINUATION FOR THE HEAT OPERATOR WITH POTENTIALS IN WEAK SPACES",

abstract = "We prove the strong unique continuation property for the differential inequality |(∂t + Δ)u(x, t)| ≤ V(x, t)|u(x, t)|, with V contained in weak spaces. In particular, we establish the strong unique continuation property for V ∈ L∞tLd/2,∞x, 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 = "Carleman estimate, Hermite operator, the heat equation, unique continuation",

author = "Eunhee Jeong and Sanghyuk Lee and Jaehyeon Ryu",

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language = "English",

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T1 - UNIQUE CONTINUATION FOR THE HEAT OPERATOR WITH POTENTIALS IN WEAK SPACES

AU - Jeong, Eunhee

AU - Lee, Sanghyuk

AU - Ryu, Jaehyeon

N1 - Publisher Copyright: © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open

PY - 2024

Y1 - 2024

N2 - We prove the strong unique continuation property for the differential inequality |(∂t + Δ)u(x, t)| ≤ V(x, t)|u(x, t)|, with V contained in weak spaces. In particular, we establish the strong unique continuation property for V ∈ L∞tLd/2,∞x, 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.

AB - We prove the strong unique continuation property for the differential inequality |(∂t + Δ)u(x, t)| ≤ V(x, t)|u(x, t)|, with V contained in weak spaces. In particular, we establish the strong unique continuation property for V ∈ L∞tLd/2,∞x, 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.

KW - Carleman estimate

KW - Hermite operator

KW - the heat equation

KW - unique continuation

UR - https://www.scopus.com/pages/publications/85202457971

U2 - 10.2140/apde.2024.17.2257

DO - 10.2140/apde.2024.17.2257

M3 - Journal article

AN - SCOPUS:85202457971

SN - 2157-5045

VL - 17

SP - 2257

EP - 2274

JO - Analysis and PDE

JF - Analysis and PDE

IS - 7

ER -

UNIQUE CONTINUATION FOR THE HEAT OPERATOR WITH POTENTIALS IN WEAK SPACES

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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