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Article Dans Une Revue Pure and Applied Analysis Année : 2020

Semiclassical resolvent estimates for Holder potentials

Georgi Vodev
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Résumé

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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Dates et versions

hal-02492811 , version 1 (27-02-2020)
hal-02492811 , version 2 (10-06-2020)
hal-02492811 , version 3 (03-08-2020)

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Georgi Vodev. Semiclassical resolvent estimates for Holder potentials. Pure and Applied Analysis, 2020, 2 (4), pp.841-860. ⟨hal-02492811v3⟩
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