Global unique continuation from a half space for the Schrödinger equation

Ihyeok Seo

doi:10.1016/j.jfa.2013.09.025

Global unique continuation from a half space for the Schrödinger equation

Ihyeok Seo

Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We obtain a global unique continuation result for the differential inequality |(i∂_t+δ)u|≤|V(x)u| in Rn+1. This is the first result on global unique continuation for the Schrödinger equation with time-independent potentials V(x) in Rn. Our method is based on a new type of Carleman estimates for the operator i∂_t+δ on Rn+1. As a corollary of the result, we also obtain a new unique continuation result for some parabolic equations.

Original language	English
Pages (from-to)	85-98
Number of pages	14
Journal	Journal of Functional Analysis
Volume	266
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2013.09.025
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

Carleman estimate
Fefferman-Phong class
Schrödinger equation
Unique continuation

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10.1016/j.jfa.2013.09.025

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abstract = "We obtain a global unique continuation result for the differential inequality |(i∂t+δ)u|≤|V(x)u| in Rn+1. This is the first result on global unique continuation for the Schr{\"o}dinger equation with time-independent potentials V(x) in Rn. Our method is based on a new type of Carleman estimates for the operator i∂t+δ on Rn+1. As a corollary of the result, we also obtain a new unique continuation result for some parabolic equations.",

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AB - We obtain a global unique continuation result for the differential inequality |(i∂t+δ)u|≤|V(x)u| in Rn+1. This is the first result on global unique continuation for the Schrödinger equation with time-independent potentials V(x) in Rn. Our method is based on a new type of Carleman estimates for the operator i∂t+δ on Rn+1. As a corollary of the result, we also obtain a new unique continuation result for some parabolic equations.

KW - Carleman estimate

KW - Fefferman-Phong class

KW - Schrödinger equation

KW - Unique continuation

UR - https://www.scopus.com/pages/publications/84886951501

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DO - 10.1016/j.jfa.2013.09.025

M3 - Article

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VL - 266

SP - 85

EP - 98

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Global unique continuation from a half space for the Schrödinger equation

Abstract

Keywords

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