Elliptic-hyperbolic systems and the Einstein equations

Annales Henri Poincare

Volumn 4, Issue 1, 2003, Pages 1-34

  Andersson, Lars ^a   Moncrief, Vincent ^b  

^a Department of Biology   (United States)

^b Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037272911     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-003-0120-1     Document Type: Article

References (17)

1. L. Andersson and V. Moncrief, On the global evolution problem in 3+1 dimensional general relativity, in preparation.
2. H. Beirão da Veiga, Structural stability and data dependence for fully nonlinear hyperbolic mixed problems, Arch. Rational Mech. Anal. 120, no. 1, 51-60 (1992).
3. _, Perturbation theorems for linear hyperbolic mixed problems and applications to the compressible Euler equations, Comm. Pure Appl. Math. 46, no. 2, 221-259 (1993).
4. Yvonne Choquet-Bruhat and James W. York, Geometrical well-posed systems for the Einstein equations, C. R. Acad. Sci. Paris Sér. I Math. 321, no. 8, 1089-1095 (1995).
5. J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10, no. 1, 1-68 (1978).
6. Helmut Friedrich and Alan Rendall, The Cauchy problem for the Einstein equations. Einstein's field equations and their physical implications, Springer, Berlin, 2000, pp. 127-223.
7. Mikhael Gromov and H. Blaine Lawson, Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. (1983), no. 58, 83-196 (1984).
8. Tosio Kato, Abstract evolution equations, linear and quasi-linear, revisited, Functional analysis and related topics, 1991 (Kyoto), Springer, Berlin, 1993, pp. 103-125.
9. Tosio Kato and Gustavo Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41, no. 7, 891-907 (1988).
10. 3+1, Ann. of Math. (2) 142, no. 1, 39-119 (1995).
11. Sergiu Klainerman and Francesco Nicolò, On local and global aspects of the Cauchy problem in general relativity, Classical Quantum Gravity 16, R73-R157 (1999).
12. A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984.
13. Richard S. Palais, Foundations of global non-linear analysis, W.A. Benjamin, Inc., New York-Amsterdam, 1968.
14. Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York, 1973, McGraw-Hill Series in Higher Mathematics.
15. Winfried Sickel, Composition operators acting on Sobolev spaces of fractional order - a survey on sufficient and necessary conditions, Function spaces, differential operators and nonlinear analysis (Paseky nad Jizerou, 1995), Prometheus, Prague, 1996, pp. 159-182.
16. Christopher D. Sogge, Lectures on nonlinear wave equations, International Press, Boston, MA, 1995.
17. Michael E. Taylor, Pseudodifferential operators and nonlinear PDE, Birkhäuser Boston Inc., Boston, MA, 1991.