A note on unique continuation for the Schrödinger equation

Sanghyuk Lee; Ihyeok Seo

doi:10.1016/j.jmaa.2011.11.067

A note on unique continuation for the Schrödinger equation

Sanghyuk Lee
, Ihyeok Seo

Seoul National University

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

12 Scopus citations

Abstract

We show a unique continuation result for the differential inequality |i∂ _tu+δu|≤|Vu|, where V is a time-dependent potential. Our results extend those in C.E. Kenig and C.D. Sogge (1988) [7] to include potentials contained in mixed norm spaces L _t ^pL _x ^s. Also, we obtain some endpoint inhomogeneous Strichartz estimates for the Schrödinger equation.

Original language	English
Pages (from-to)	461-468
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	389
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.11.067
State	Published - 1 May 2012
Externally published	Yes

Keywords

Schrödinger equation
Strichartz estimate
Unique continuation

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10.1016/j.jmaa.2011.11.067

Cite this

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abstract = "We show a unique continuation result for the differential inequality |i∂ tu+δu|≤|Vu|, where V is a time-dependent potential. Our results extend those in C.E. Kenig and C.D. Sogge (1988) [7] to include potentials contained in mixed norm spaces L t pL x s. Also, we obtain some endpoint inhomogeneous Strichartz estimates for the Schr{\"o}dinger equation.",

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AB - We show a unique continuation result for the differential inequality |i∂ tu+δu|≤|Vu|, where V is a time-dependent potential. Our results extend those in C.E. Kenig and C.D. Sogge (1988) [7] to include potentials contained in mixed norm spaces L t pL x s. Also, we obtain some endpoint inhomogeneous Strichartz estimates for the Schrödinger equation.

KW - Schrödinger equation

KW - Strichartz estimate

KW - Unique continuation

UR - https://www.scopus.com/pages/publications/84855855593

U2 - 10.1016/j.jmaa.2011.11.067

DO - 10.1016/j.jmaa.2011.11.067

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VL - 389

SP - 461

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

A note on unique continuation for the Schrödinger equation

Abstract

Keywords

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