Smoothing - Strichartz estimates for the schrödinger equation with small magnetic potential

Vladimir Georgiev; Atanas Stefanov; Mirko Tarulli

doi:10.3934/dcds.2007.17.771

Smoothing - Strichartz estimates for the schrödinger equation with small magnetic potential

Vladimir Georgiev^*, Atanas Stefanov, Mirko Tarulli

^*Corresponding author for this work

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

32 Citations (Scopus)

Abstract

The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too.

Original language	English
Pages (from-to)	771-786
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems
Volume	17
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2007.17.771
Publication status	Published - 2007 Apr
Externally published	Yes

Keywords

Schrödinger equation
Smoothing properties
Strichartz estimates

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2007.17.771

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title = "Smoothing - Strichartz estimates for the schr{\"o}dinger equation with small magnetic potential",

abstract = "The work treats smoothing and dispersive properties of solutions to the Schr{\"o}dinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too.",

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author = "Vladimir Georgiev and Atanas Stefanov and Mirko Tarulli",

year = "2007",

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T1 - Smoothing - Strichartz estimates for the schrödinger equation with small magnetic potential

AU - Georgiev, Vladimir

AU - Stefanov, Atanas

AU - Tarulli, Mirko

PY - 2007/4

Y1 - 2007/4

N2 - The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too.

AB - The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too.

KW - Schrödinger equation

KW - Smoothing properties

KW - Strichartz estimates

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M3 - Article

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SP - 771

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 4

ER -

Smoothing - Strichartz estimates for the schrödinger equation with small magnetic potential

Abstract

Keywords

ASJC Scopus subject areas

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