Uniqueness results for Ill-posed characteristic problems in curved space-times

Communications in Mathematical Physics

Volumn 285, Issue 3, 2009, Pages 873-900

  Ionescu, Alexandru D ^a   Klainerman, Sergiu ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58149494382     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0650-y     Document Type: Article

References (21)

1. S. Alinhac M.S. Baouendi 1995 A non-uniqueness result for operators of principal type Math. Z. 220 561 568
2. Carleman, T.: Sur un probleme d'unicite pour les systemes d'equations aux derivees partielles a deux variables independantes. Ark. Mat., Astr. Fys. 26 (1939)
3. B. Carter 1971 An axy-symmetric black hole has only two degrees of freedom Phys. Rev. Lett. 26 331 333
4. Chandrasekhar, S.: The mathematical theory of black holes. International Series of Monographs on Physics, 69, Oxford Science Publications, New York: The Clarendon Press/Oxford University Press, 1983
5. Cohen, P.: The non-uniqueness of the Cauchy problem. ONR Technical Report, 93, Stanford Univ., 1960
6. F.G. Friedlander 1967 On an improperly posed characteristic initial value problem J. Math. Mech. 16 907 915
7. F.G. Friedlander 1973 An inverse problem for radiation fields Proc. London Math. Soc. 27 551 576
8. F. John 1949 On linear partial differential equations with analytic coefficients Unique continuation of Data. Comm. Pure Appl. Math. 2 209 253
9. John F.: Partial Differential Equations. Fourth edition, Springer- Verlag, Berlin-Heidelberg-New York (1991)
10. Hawking S.W., Ellis G.F.R.: The large scale structure of space-time. Fourth edition, Cambridge Univ. Press, Cambridge (1973)
11. Hörmander, L.: On the uniqueness of the Cauchy problem under partial analyticity assumptions. In: Geometrical optics and related topics (Cortona, 1996), Progr. Nonlinear Differential Equations Appl., 32, Boston, MA: Birkhäuser Boston, 1997, pp. 179-219
12. Hörmander, L.: Non-uniqueness for the Cauchy problem. Lect. Notes in Math., 459, Berlin-Heidelberg-New York: Springer Verlag, 1975, pp. 36-72
13. Hörmander L.: The analysis of linear partial differential operators. Springer-Verlag, Berlin (1985)
14. Ionescu, A., Klainerman, S.: On the uniqueness of smooth, stationary black holes in vacuum. http://arXiv.org/abs/0711.0040v2[gr.gc], 2008
15. V. Isakov 1993 Carleman type estimates in an anisotropic case and applications J. Diff. Eqs. 105 217 238
16. C.E. Kenig A. Ruiz C.D. Sogge 1987 Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators Duke Math. J. 55 329 347
17. M. Mars 1999 A spacetime characterization of the Kerr metric Class. Quant. Grav. 16 2507 2523
18. F. Pretorius W. Israel 1989 Quasi-spherical light cones of the Kerr geometry Class. Quant. Grav. 15 2289 2301
19. L. Robbiano C. Zuily 1998 Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients Invent. Math. 131 493 539
20. D.C. Robinson 1975 Uniqueness of the Kerr black hole Phys. Rev. Lett. 34 905 906
21. D. Tataru 1999 Unique continuation for operators with partially analytic coefficients J. Math. Pures Appl. 78 505 521