$L^{\infty}- L^{2}$ weighted estimate for the wave equation with potential

Georgiev, Vladimir; Visciglia, Nicola

L^{\infty} - L^{2}

weighted estimate for the wave equation with potential

Georgiev, Vladimir ; Visciglia, Nicola

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 14 (2003), p. 109-135 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

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 $V \geq 0$ satisfies $|V (x)| \leq \frac{C}{{(1 + |x|)}^{2 + ϵ_{0}}},$ where $ϵ_{0} > 0$ .

Si considera l’equazione delle onde perturbata con un potenziale in dimensione tre e si provano delle stime dispersive per il propagatore associato. La stima principale è ottenuta sotto la condizione che il potenziale $V \geq 0$ soddisfi $|V (x)| \leq \frac{C}{{(1 + |x|)}^{2 + ϵ_{0}}},$ dove $ϵ_{0} > 0$ .

Publié le : 2003-06-01

MR 2053661 | Zbl 1072.35111

@article{RLIN_2003_9_14_2_109_0,
     author = {Vladimir Georgiev and Nicola Visciglia},
     title = {$L^{\infty}- L^{2}$ weighted estimate for the wave equation with potential},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {14},
     year = {2003},
     pages = {109-135},
     zbl = {1072.35111},
     mrnumber = {2053661},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2003_9_14_2_109_0}
}

Georgiev, Vladimir; Visciglia, Nicola. $L^{\infty}- L^{2}$ weighted estimate for the wave equation with potential. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 14 (2003) pp. 109-135. http://gdmltest.u-ga.fr/item/RLIN_2003_9_14_2_109_0/

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