weighted estimate for the wave equation with potential
Vladimir Georgiev; Nicola Visciglia
- Volume: 14, Issue: 2, page 109-135
- ISSN: 1120-6330
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topGeorgiev, Vladimir, and 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 14.2 (2003): 109-135. <http://eudml.org/doc/252280>.
@article{Georgiev2003,
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 $V \ge 0$ satisfies
$$|V(x)| \le \frac\{C\}\{(1+ |x|)^\{2+\epsilon\_\{0\}\}\},$$
where $\epsilon_\{0\} > 0$.},
author = {Georgiev, Vladimir, Visciglia, Nicola},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Perturbed wave equation; Resolvent estimates; Spectral theory; Fredholm theory},
language = {eng},
month = {6},
number = {2},
pages = {109-135},
publisher = {Accademia Nazionale dei Lincei},
title = {$L^\{\infty\}- L^\{2\}$ weighted estimate for the wave equation with potential},
url = {http://eudml.org/doc/252280},
volume = {14},
year = {2003},
}
TY - JOUR
AU - Georgiev, Vladimir
AU - Visciglia, Nicola
TI - $L^{\infty}- L^{2}$ weighted estimate for the wave equation with potential
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/6//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 2
SP - 109
EP - 135
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 $V \ge 0$ satisfies
$$|V(x)| \le \frac{C}{(1+ |x|)^{2+\epsilon_{0}}},$$
where $\epsilon_{0} > 0$.
LA - eng
KW - Perturbed wave equation; Resolvent estimates; Spectral theory; Fredholm theory
UR - http://eudml.org/doc/252280
ER -
References
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