Asymptotic behaviour of the scattering phase in linear elasticity II

Osaka Journal of Mathematics

Volumn 35, Issue 2, 1998, Pages 397-405

  Cardoso, Fernando ^a   Vodev, Georgi ^b  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b Universite de Nantes   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038855306     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. F. Cardoso and G. Vodev: Asymptotic behaviour of the scattering phase in linear elasticity for a strictly convex body, Comm. in Partial Diff. Equations, 22 (1997), 2025-2049.
2. M. Dimassi and J. Sjöstrand: Trace asymptotics via almost analytic extensions, in: Partial Differential Equations and Mathematical Physics, The Danish - Swedish Analysis Seminar, 1995, L. Hörmander and A. Melin, eds. Birkhäuser, Boston, 1996, 126-142.
3. V. Ivrii: On the second term in the spectral asymptotic for the Laplace-Beltrami operator on a manifold with boundary, Funct. Anal. Appl. 4 (1980), 98-106.
4. M. Kawashita: On a region free from the poles of the resolvent and decay rate of the local energy for the elastic wave equation, Indiana Univ. Math. J. 43 (1994), 1013-1043.
5. A. Majda and J.V. Ralston: An analogue of Weyl's theorem for unbounded domains I, II, III, Duke Math. J. 45 (1978), 183-196; Duke Math. J. 45 (1978), 513-536; Duke Math. J. 46 (1979), 725-731.
6. A. Majda and J.V. Ralston: An analogue of Weyl's theorem for unbounded domains I, II, III, Duke Math. J. 45 (1978), 183-196; Duke Math. J. 45 (1978), 513-536; Duke Math. J. 46 (1979), 725-731.
7. A. Majda and J.V. Ralston: An analogue of Weyl's theorem for unbounded domains I, II, III, Duke Math. J. 45 (1978), 183-196; Duke Math. J. 45 (1978), 513-536; Duke Math. J. 46 (1979), 725-731.
8. R.B. Melrose: Scattering theory and the trace of the wave group, J. Funct. Anal. 45 (1982), 29-40.
9. R.B. Melrose: The trace of the wave group, Contemporary Math. 27 (1984), 127-167.
10. R.B. Melrose: Weyl asymptotic for the phase in obstacle scattering, Comm. in Partial Diff. Equations, 13 (1988), 1431-1439.
11. V. Petkov and G. Popov: Asymptotic behaviour of the scattering phase for nontrapping obstacles, Ann. Inst. Fourier Grenoble, 32 (1982), 111-149.
12. D. Robert: On the Weyl formula for obstacles, in: Partial Differential Equations and Mathematical Physics, The Danish - Swedish Analysis Seminar, 1995, L. Hörmander and A. Melin, eds., Birkhäuser, Boston, 1996, 262-285.
13. Yu. Safarov and D. Vassiliev: Branching Hamiltonian billiards, Soviet Math. Dokl. 38 (1989), 64-68.
14. Yu. Safarov and D. Vassiliev: The asymptotic distribution of eigenvalues of partial differential operators, Translations of Math. Monographs, American Math. Soc. 155 (1996).
15. J. Sjöstrand and G. Vodev: Asymptotics of the number of Rayleigh resonances, Math. Ann. 309 (1997), 287-306.
16. J. Sjöstrand and M. Zworski: Lower bounds on the number of scattering poles. II, J. Funct. Anal. 123 (1994), 336-367.
17. P. Stefanov and G. Vodev: Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body, Duke Math. J. 78 (1995), 677-714.
18. P. Stefanov and G. Vodev: Neumann resonances in linear elasticity for an arbitrary body, Commun. Math. Phys. 176 (1996), 645-659.
19. D. Vassiliev: Two-term asymptotics of the spectrum of a boundary value problem under an interior reflection of general form, Funct. Anal. Appl. 18 (1984), 267-277.
20. D. Vassiliev: Two-term asymptotics of the spectrum of a boundary value problem in the case of a piecewise smooth boundary, Soviet Math. Dokl. 33 (1986), 227-230.
21. G. Vodev: Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Commun. Math. Phys. 146 (1992), 205-216.
22. G. Vodev: Existence of Rayleigh resonances exponentially close to the real axis, Ann. Inst. H. Poincaré (Physique Théorique), 67 (1997), 41-57.