Georgiev, Vladimir and Visciglia, Nicola:
$L^{\infty}- L^{2}$ weighted estimate for the wave equation with potential (Stime $L^{\infty}- L^{2}$ pesate per l’equazione delle onde con potenziale)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 14 (2003), fasc. n.2, p. 109-135, (English)
pdf (568 Kb), djvu (298 Kb). | MR2053661 | Zbl 1072.35111
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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 $V \ge 0$ soddisfi
$$|V(x)| \le \frac{C}{(1+ |x|)^{2+\epsilon_{0}}},$$
dove $\epsilon_{0} > 0$.
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Con il contributo del Ministero per i Beni e le Attività Culturali