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September 2020 Decay of local energy for solutions of the free Schrödinger equation in exterior domains
N. Burq, B. Ducomet
Kyoto J. Math. 60(3): 911-939 (September 2020). DOI: 10.1215/21562261-2019-0050

Abstract

In this article, we study the decay of the solutions of Schrödinger equations in the exterior of an obstacle. The main situations we are interested in are the general case (no nontrapping assumptions) and some weakly trapping situations.

On s’intéresse dans cet article à la décroissance temporelle de la solution du problème extérieur pour l’équation de Schrödinger, dans le cas d’obstacles. Les situations auquelles on s’intéresse sont le cas général (pas d’hypothèse géométrique) ou alors des situations faiblement captantes.

Citation

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N. Burq. B. Ducomet. "Decay of local energy for solutions of the free Schrödinger equation in exterior domains." Kyoto J. Math. 60 (3) 911 - 939, September 2020. https://doi.org/10.1215/21562261-2019-0050

Information

Received: 15 September 2015; Revised: 20 March 2017; Accepted: 29 January 2018; Published: September 2020
First available in Project Euclid: 12 August 2020

MathSciNet: MR4134353
Digital Object Identifier: 10.1215/21562261-2019-0050

Subjects:
Primary: 35B37
Secondary: 35J15, 47F05

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 3 • September 2020
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