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Weighted energy estimates for wave equations in exterior domains
-
Mishio Kawashita
and
Hiroshi Sugimoto
Published/Copyright:
June 27, 2010
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.
Keywords.: Wave equations; weighted energy estimates; local energy decay; Keel; Smith and Sogge estimate
Received: 2009-01-27
Revised: 2009-11-09
Published Online: 2010-06-27
Published in Print: 2011-November
© de Gruyter 2011
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Keywords for this article
Wave equations;
weighted energy estimates;
local energy decay;
Keel;
Smith and Sogge estimate
Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
- Heegner points and Eisenstein series
- Discrete components of some complementary series
- Even universal binary Hermitian lattices over imaginary quadratic fields
- Combinatorial classification of piecewise hereditary algebras
- Weighted energy estimates for wave equations in exterior domains
- Invariant sets and ergodic decomposition of local semi-Dirichlet forms
- Regularity in parabolic Dini continuous systems
- The reciprocity law for the twisted second moment of Dirichlet L-functions
