Vol. 2, No. 4, 2020

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Semiclassical resolvent estimates for Hölder potentials

Georgi Vodev

Vol. 2 (2020), No. 4, 841–860
Abstract

We first prove semiclassical resolvent estimates for the Schrödinger operator in 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 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.

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