메뉴 건너뛰기




Volumn 282, Issue 3, 2008, Pages 697-719

Decay and non-decay of the local energy for the wave equation on the De Sitter-Schwarzschild metric

Author keywords

[No Author keywords available]

Indexed keywords


EID: 49049095022     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0553-y     Document Type: Article
Times cited : (139)

References (34)
  • 1
    • 48249090455 scopus 로고    scopus 로고
    • Semiclassical scattering amplitude at the maximum point of the potential
    • 1-2
    • I. Alexandrova J.-F. Bony T. Ramond 2008 Semiclassical scattering amplitude at the maximum point of the potential Asymptotic Analysis 58 1-2 57 125
    • (2008) Asymptotic Analysis , vol.58 , pp. 57-125
    • Alexandrova, I.1    Bony, J.-F.2    Ramond, T.3
  • 2
    • 0003288140 scopus 로고    scopus 로고
    • 0 -groups, commutator methods and spectral theory of N-body Hamiltonians
    • Basel-Boston: Birkhäuser Verlag
    • 0 -groups, commutator methods and spectral theory of N-body Hamiltonians, Progress in Mathematics, Vol. 135, Basel-Boston: Birkhäuser Verlag, 1996
    • (1996) Progress in Mathematics , vol.135
    • Amrein, W.1    Boutet De Monvel, A.2    Georgescu, V.3
  • 5
    • 33749992424 scopus 로고    scopus 로고
    • Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space
    • 2
    • P. Blue J. Sterbenz 2006 Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space Commun. Math. Phys. 268 2 481 504
    • (2006) Commun. Math. Phys. , vol.268 , pp. 481-504
    • Blue, P.1    Sterbenz, J.2
  • 6
    • 2142824978 scopus 로고    scopus 로고
    • Microlocalization of resonant states and estimates of the residue of the scattering amplitude
    • 2
    • J.-F. Bony L. Michel 2004 Microlocalization of resonant states and estimates of the residue of the scattering amplitude Commun. Math. Phys. 246 2 375 402
    • (2004) Commun. Math. Phys. , vol.246 , pp. 375-402
    • Bony, J.-F.1    Michel, L.2
  • 7
    • 3142714420 scopus 로고    scopus 로고
    • Smoothing effect for Schrödinger boundary value problems
    • 2
    • N. Burq 2004 Smoothing effect for Schrödinger boundary value problems Duke Math. J. 123 2 403 427
    • (2004) Duke Math. J. , vol.123 , pp. 403-427
    • Burq, N.1
  • 8
    • 0035537365 scopus 로고    scopus 로고
    • Resonance expansions in semi-classical propagation
    • 1
    • N. Burq M. Zworski 2001 Resonance expansions in semi-classical propagation Commun. Math. Phys. 223 1 1 12
    • (2001) Commun. Math. Phys. , vol.223 , pp. 1-12
    • Burq, N.1    Zworski, M.2
  • 9
    • 17744379966 scopus 로고
    • The mathematical theory of black holes
    • The Clarendon Press, Oxford: Oxford University Press
    • Chandrasekhar, S.: The mathematical theory of black holes. International Series of Monographs on Physics, Vol. 69, The Clarendon Press, Oxford: Oxford University Press, 1992
    • (1992) International Series of Monographs on Physics , vol.69
    • Chandrasekhar, S.1
  • 10
    • 0034349028 scopus 로고    scopus 로고
    • Resonance wave expansions: Two hyperbolic examples
    • 2
    • T. Christiansen M. Zworski 2000 Resonance wave expansions: two hyperbolic examples Commun. Math. Phys. 212 2 323 336
    • (2000) Commun. Math. Phys. , vol.212 , pp. 323-336
    • Christiansen, T.1    Zworski, M.2
  • 11
    • 0003333181 scopus 로고
    • The global nonlinear stability of the Minkowski space
    • Princeton, NJ: Princeton University Press
    • Christodoulou, D., Klainerman, S.: The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, Vol. 41, Princeton, NJ: Princeton University Press, 1993
    • (1993) Princeton Mathematical Series , vol.41
    • Christodoulou, D.1    Klainerman, S.2
  • 12
    • 26444568141 scopus 로고    scopus 로고
    • A proof of Price's law for the collapse of a self-gravitating scalar field
    • 2
    • M. Dafermos I. Rodnianski 2005 A proof of Price's law for the collapse of a self-gravitating scalar field Invent. Math. 162 2 381 457
    • (2005) Invent. Math. , vol.162 , pp. 381-457
    • Dafermos, M.1    Rodnianski, I.2
  • 13
    • 33646002667 scopus 로고    scopus 로고
    • Decay of solutions of the wave equation in the Kerr geometry
    • 2
    • F. Finster N. Kamran J. Smoller S.-T. Yau 2006 Decay of solutions of the wave equation in the Kerr geometry Commun. Math. Phys. 264 2 465 503
    • (2006) Commun. Math. Phys. , vol.264 , pp. 465-503
    • Finster, F.1    Kamran, N.2    Smoller, J.3    Yau, S.-T.4
  • 14
    • 24144449996 scopus 로고    scopus 로고
    • Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
    • Guillarmou, C.: Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds. Duke Math. J. 129(1), 1-37 (2005)
    • (2005) Duke Math. J. , vol.129 , Issue.1 , pp. 1-37
    • Guillarmou, C.1
  • 15
    • 84972552788 scopus 로고
    • Decay of solutions of the wave equation in the exterior of two convex obstacles
    • 3
    • M. Ikawa 1982 Decay of solutions of the wave equation in the exterior of two convex obstacles Osaka J. Math. 19 3 459 509
    • (1982) Osaka J. Math. , vol.19 , pp. 459-509
    • Ikawa, M.1
  • 16
    • 0041110085 scopus 로고
    • Scattering theory
    • Second ed. With appendices by C. Morawetz and G. Schmidt London-New York: Academic Press Inc.
    • Lax, P., Phillips, R.: Scattering theory, Second ed. With appendices by C. Morawetz and G. Schmidt Pure and Applied Mathematics, Vol. 26, London-New York: Academic Press Inc., 1989
    • (1989) Pure and Applied Mathematics , vol.26
    • Lax, P.1    Phillips, R.2
  • 17
    • 0036025585 scopus 로고    scopus 로고
    • Resonance free domains for non globally analytic potentials
    • 4
    • A. Martinez 2002 Resonance free domains for non globally analytic potentials Ann. Henri Poincaré 3 4 739 756
    • (2002) Ann. Henri Poincaré , vol.3 , pp. 739-756
    • Martinez, A.1
  • 18
    • 0001189870 scopus 로고
    • Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
    • 2
    • R. Mazzeo R. Melrose 1987 Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature J. Funct. Anal. 75 2 260 310
    • (1987) J. Funct. Anal. , vol.75 , pp. 260-310
    • Mazzeo, R.1    Melrose, R.2
  • 20
    • 33846062287 scopus 로고
    • Absence of singular continuous spectrum for certain selfadjoint operators
    • 3
    • E. Mourre 1980 Absence of singular continuous spectrum for certain selfadjoint operators Commun. Math. Phys. 78 3 391 408
    • (1980) Commun. Math. Phys. , vol.78 , pp. 391-408
    • Mourre, E.1
  • 21
    • 0346899470 scopus 로고    scopus 로고
    • Resonance expansions of propagators in the presence of potential barriers
    • 1
    • S. Nakamura P. Stefanov M. Zworski 2003 Resonance expansions of propagators in the presence of potential barriers J. Funct. Anal. 205 1 180 205
    • (2003) J. Funct. Anal. , vol.205 , pp. 180-205
    • Nakamura, S.1    Stefanov, P.2    Zworski, M.3
  • 22
    • 84981752412 scopus 로고
    • Solutions of the wave equation with localized energy
    • J. Ralston 1969 Solutions of the wave equation with localized energy Commun. Pure Appl. Math. 22 807 823
    • (1969) Commun. Pure Appl. Math. , vol.22 , pp. 807-823
    • Ralston, J.1
  • 25
    • 0031539570 scopus 로고    scopus 로고
    • Distribution of resonances for spherical black holes
    • 1
    • A. Sá Barreto M. Zworski 1997 Distribution of resonances for spherical black holes Math. Res. Lett. 4 1 103 121
    • (1997) Math. Res. Lett. , vol.4 , pp. 103-121
    • Sá Barreto, A.1    Zworski, M.2
  • 26
    • 0005546811 scopus 로고
    • Semiclassical resonances generated by nondegenerate critical points
    • Pseudodifferential operators (Oberwolfach, 1986) Berlin-Heidelberg-New York: Springer
    • Sjöstrand, J.: Semiclassical resonances generated by nondegenerate critical points. In: Pseudodifferential operators (Oberwolfach, 1986), Lecture Notes in Math., Vol. 1256, Berlin-Heidelberg-New York: Springer, 1987, pp. 402-429
    • (1987) Lecture Notes in Math. , vol.1256 , pp. 402-429
    • Sjöstrand, J.1
  • 27
    • 0001047998 scopus 로고    scopus 로고
    • A trace formula and review of some estimates for resonances, Microlocal analysis and spectral theory (Lucca, 1996)
    • Dordrecht: Kluwer Acad. Publ.
    • Sjöstrand, J.: A trace formula and review of some estimates for resonances, Microlocal analysis and spectral theory (Lucca, 1996), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 490, Dordrecht: Kluwer Acad. Publ., 1997, pp. 377-437
    • (1997) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.490 , pp. 377-437
    • Sjöstrand, J.1
  • 28
    • 33751083232 scopus 로고    scopus 로고
    • Preprint available on
    • Sjöstrand, J.: Lectures on resonances. Preprint available on http://www.math.polytechnique.fr/∼sjoestrand, 2007, pp. 1-169
    • (2007) Lectures on Resonances , pp. 1-169
    • Sjöstrand, J.1
  • 29
    • 84968505435 scopus 로고
    • Complex scaling and the distribution of scattering poles
    • 4
    • J. Sjöstrand M. Zworski 1991 Complex scaling and the distribution of scattering poles J. Amer. Math. Soc. 4 4 729 769
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 729-769
    • Sjöstrand, J.1    Zworski, M.2
  • 30
    • 0032219326 scopus 로고    scopus 로고
    • From quasimodes to resonances
    • 3
    • S.-H. Tang M. Zworski 1998 From quasimodes to resonances Math. Res. Lett. 5 3 261 272
    • (1998) Math. Res. Lett. , vol.5 , pp. 261-272
    • Tang, S.-H.1    Zworski, M.2
  • 31
    • 0034375059 scopus 로고    scopus 로고
    • Resonance expansions of scattered waves
    • 10
    • S.-H. Tang M. Zworski 2000 Resonance expansions of scattered waves Comm. Pure Appl. Math. 53 10 1305 1334
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1305-1334
    • Tang, S.-H.1    Zworski, M.2
  • 34
    • 0033473946 scopus 로고    scopus 로고
    • Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces
    • 2
    • M. Zworski 1999 Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces Invent. Math. 136 2 353 409
    • (1999) Invent. Math. , vol.136 , pp. 353-409
    • Zworski, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.