Unique continuation for the schrödinger equation with gradient term

Youngwoo Koh; Ihyeok Seo

doi:10.1090/proc/13942

Unique continuation for the schrödinger equation with gradient term

Youngwoo Koh
, Ihyeok Seo

Department of Mathematics

Kongju National University

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

1 Scopus citations

Abstract

We obtain a unique continuation result for the differential inequality |(i∂_t + Δ)u| ≤ |V u| + |W · ∇u| by establishing L² Carleman estimates. Here, V is a scalar function and W is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrödinger equation.

Original language	English
Pages (from-to)	2555-2562
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	6
DOIs	https://doi.org/10.1090/proc/13942
State	Published - 2018

Keywords

Carleman estimates
Schrödinger equation
Unique continuation

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10.1090/proc/13942

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title = "Unique continuation for the schr{\"o}dinger equation with gradient term",

abstract = "We obtain a unique continuation result for the differential inequality |(i∂t + Δ)u| ≤ |V u| + |W · ∇u| by establishing L2 Carleman estimates. Here, V is a scalar function and W is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schr{\"o}dinger equation.",

keywords = "Carleman estimates, Schr{\"o}dinger equation, Unique continuation",

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AU - Koh, Youngwoo

AU - Seo, Ihyeok

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N2 - We obtain a unique continuation result for the differential inequality |(i∂t + Δ)u| ≤ |V u| + |W · ∇u| by establishing L2 Carleman estimates. Here, V is a scalar function and W is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrödinger equation.

AB - We obtain a unique continuation result for the differential inequality |(i∂t + Δ)u| ≤ |V u| + |W · ∇u| by establishing L2 Carleman estimates. Here, V is a scalar function and W is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrödinger equation.

KW - Carleman estimates

KW - Schrödinger equation

KW - Unique continuation

UR - https://www.scopus.com/pages/publications/85044366688

U2 - 10.1090/proc/13942

DO - 10.1090/proc/13942

M3 - Article

AN - SCOPUS:85044366688

SN - 0002-9939

VL - 146

SP - 2555

EP - 2562

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Unique continuation for the schrödinger equation with gradient term

Abstract

Keywords

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