Semiclassical resolvent estimates for Hölder potentials

We first prove semiclassical resolvent estimates for the Schrödinger operator in $ℝ^{d}$ , $d \geq 3$ , with real-valued potentials which are Hölder with respect to the radial variable. Then we extend these resolvent estimates to exterior domains in $ℝ^{d}$ , $d \geq 2$ , 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 $L^{\infty}$ .

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Keywords

Schrödinger operator, resolvent estimates, Hölder potentials

Mathematical Subject Classification 2010

Primary: 35P25

Milestones

Received: 6 March 2020

Revised: 30 June 2020

Accepted: 4 August 2020

Published: 25 February 2021

Authors

Georgi Vodev
Département de Mathématiques Laboratoire de Mathématiques Jean Leray Université de Nantes France

Vol. 2, No. 4, 2020

Georgi Vodev

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors