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1 June 2004 Smoothing effect for Schrödinger equations
N. Burq
Duke Math. J. 123(2): 403-427 (1 June 2004). DOI: 10.1215/S0012-7094-04-12326-7

Abstract

We show the necessity of the nontrapping condition for the plain smoothing effect ($H^{1/2}$) for the Schrödinger equation with Dirichlet boundary conditions in exterior problems. We also give a class of trapped obstacles (Ikawa's example) for which we can prove a weak ($H^{1/2 - \varepsilon}$) smoothing effect.

On démontre que l'hypothèse de non capture est nécessaire pour l'effet régularisant ($H^{1/2}$) pour l'équation de Schrödinger avec conditions aux limites de Dirichlet à l'extérieur d'un domaine de $\mathbb{R}^d$. On donne aussi une classe d'obstacles captifs (l'exemple d'Ikawa) pour lesquels on démontre un effet régularisant affaibli ($H^{1/2 - \varepsilon}$).

Citation

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N. Burq. "Smoothing effect for Schrödinger equations." Duke Math. J. 123 (2) 403 - 427, 1 June 2004. https://doi.org/10.1215/S0012-7094-04-12326-7

Information

Published: 1 June 2004
First available in Project Euclid: 11 June 2004

zbMATH: 1061.35024
MathSciNet: MR2066943
Digital Object Identifier: 10.1215/S0012-7094-04-12326-7

Subjects:
Primary: 60F05
Secondary: 05E05 , 05E10 , 33E17 , 47B35

Rights: Copyright © 2004 Duke University Press

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Vol.123 • No. 2 • 1 June 2004
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