Semiclassical resolvent estimates for Holder potentials

2020/02/28 by Georgi Vodev, Vodev, Georgi · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2002.12853

Abstract

We first prove semiclassical resolvent estimates for the Schrödinger operator in R d , d ≥ 3, with real-valued potentials which are Hölder with respect to the radial variable. Then we extend these resolvent estimates to exterior domains in R d , d ≥ 2, and real-valued potentials which are Hölder 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 Hölder, Lipschitz or just L ∞ .

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