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ID 33924
file
creator
Sugimoto, Hiroshi
subject
Wave equations
weighted energy estimates
local energy decay
Keel
Smith and Sogge estimate
2010 Mathematics Subject Classification: 35L05
2010 Mathematics Subject Classification: 35P25
2010 Mathematics Subject Classification: 35B40
NDC
Mathematics
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 title
Forum Mathematicum
volume
Volume 23
issue
Issue 6
start page
1217
end page
1258
date of issued
2011
publisher
Walter De Gruyter & Co.
issn
0933-7741
ncid
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
publisher
rights
(c) de Gruyter 2011
relation url
department
Graduate School of Science