L∞ - L2 weighted estimate for the wave equation with potential

Vladimir Georgiev; Nicola Visciglia

L^∞ - L² weighted estimate for the wave equation with potential

Research output: Contribution to journal › Article

Abstract

We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential V≥ satisfies |V_(x)|≤^C/_(1+|x|)2+ε0.

Original language	English
Pages (from-to)	109-135
Number of pages	27
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume	14
Issue number	2
Publication status	Published - 2003 Dec 1
Externally published	Yes

Keywords

Fredholm theory
Perturbed wave equation
Resolvent estimates
Spectral theory

ASJC Scopus subject areas

Mathematics(all)

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title = "L∞ - L2 weighted estimate for the wave equation with potential",

abstract = "We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential V≥ satisfies |V(x)|≤C/(1+|x|)2+ε0.",

keywords = "Fredholm theory, Perturbed wave equation, Resolvent estimates, Spectral theory",

author = "Vladimir Georgiev and Nicola Visciglia",

year = "2003",

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journal = "Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni",

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T1 - L∞ - L2 weighted estimate for the wave equation with potential

AU - Georgiev, Vladimir

AU - Visciglia, Nicola

PY - 2003/12/1

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N2 - We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential V≥ satisfies |V(x)|≤C/(1+|x|)2+ε0.

AB - We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential V≥ satisfies |V(x)|≤C/(1+|x|)2+ε0.

KW - Fredholm theory

KW - Perturbed wave equation

KW - Resolvent estimates

KW - Spectral theory

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EP - 135

JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

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