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Weighted energy estimates for wave equations in exterior domains

Weighted energy estimates for wave equations in exterior domains Weighted energy estimates including the Keel, Smith and Sogge estimate is obtained for solutions of exterior problem of the wave equation in three or higher dimensional Euclidean spaces. For the solutions of the Cauchy problem, which is corresponding to the free system in scattering theory, the estimates are given by using the ideas introduced by Morawetz and summarized by Mochizuki for the Dirichlet problem in the outside of star shaped obstacles. From the estimates for the free system, the corresponding estimates for exterior domains are given if it is assumed that the local energy decays uniformly with respect to initial data, which depends on the structures of propagation of singularities. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Weighted energy estimates for wave equations in exterior domains

Forum Mathematicum , Volume 23 (6) – Nov 1, 2011

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References (31)

Publisher
de Gruyter
Copyright
© de Gruyter 2011
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORM.2011.045
Publisher site
See Article on Publisher Site

Abstract

Weighted energy estimates including the Keel, Smith and Sogge estimate is obtained for solutions of exterior problem of the wave equation in three or higher dimensional Euclidean spaces. For the solutions of the Cauchy problem, which is corresponding to the free system in scattering theory, the estimates are given by using the ideas introduced by Morawetz and summarized by Mochizuki for the Dirichlet problem in the outside of star shaped obstacles. From the estimates for the free system, the corresponding estimates for exterior domains are given if it is assumed that the local energy decays uniformly with respect to initial data, which depends on the structures of propagation of singularities.

Journal

Forum Mathematicumde Gruyter

Published: Nov 1, 2011

Keywords: Wave equations; weighted energy estimates; local energy decay; Keel; Smith and Sogge estimate

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