Weighted energy estimates for wave equations in exterior domains
FORM.2011.pdf 401 KB
weighted energy estimates
local energy decay
Smith and Sogge estimate
2010 Mathematics Subject Classification: 35L05
2010 Mathematics Subject Classification: 35P25
2010 Mathematics Subject Classification: 35B40
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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Walter De Gruyter & Co.
(c) de Gruyter 2011
Graduate School of Science