Semiclassical resolvent estimates for Holder potentials

Georgi Vodev

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arXiv · 2002.12853

Semiclassical resolvent estimates for Holder potentials

Georgi Vodev

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Abstract

We first prove semiclassical resolvent estimates for the Schr{\"o}dinger operator in R d , d $\ge$ 3, with real-valued potentials which are H{\"o}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{\"o}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{\"o}lder, Lipschitz or just L $\infty$ .

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Georgi Vodev. 2020-02-28. Semiclassical resolvent estimates for Holder potentials. https://arxiv.org/abs/2002.12853

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