Weighted energy estimates for wave equations in exterior domains
Forum Mathematicum Volume 23 Issue 6
Page 1217-1258
published_at 2011
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| File | |
| Title ( eng ) |
Weighted energy estimates for wave equations in exterior domains
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| Creator |
Sugimoto Hiroshi
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| Source Title |
Forum Mathematicum
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| Volume | 23 |
| Issue | 6 |
| Start Page | 1217 |
| End Page | 1258 |
| 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.
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| Keywords |
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
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Walter De Gruyter & Co.
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| Date of Issued | 2011 |
| Rights |
(c) de Gruyter 2011
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| Publish Type | Version of Record |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0933-7741
[DOI] 10.1515/FORM.2011.045
[NCID] AA10669403
[DOI] http://dx.doi.org/10.1515/FORM.2011.045
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