Year: 2020
Type: preprint
Abstract: We first prove semiclassical resolvent estimates for the Schr{ö}dinger operator in R d , d $\ge$ 3, with real-valued potentials which are H{ö}lder with respect to the radial variable. Then we extend these resolvent estimates to exterior domains in R d , d $\ge$ 2, and real-valued potentials which are H{ö}lder with respect to the space variable. As an application, we obtain the rate of the decay of the local energy of the solutions to the wave equation with a refraction index which may be H{ö}lder, Lipschitz or just L $\infty$ .
Source: arXiv (Cornell University)
Author: Vodev, Georgi
Institution: Laboratoire de Mathématiques Jean Leray
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3008035791