Cauchy data on a manifold

Yvonne Choquet-Bruhat; Demetrios Christodoulou; Mauro Francaviglia

Annales de l'I.H.P. Physique théorique (1978)

  • Volume: 29, Issue: 3, page 241-255
  • ISSN: 0246-0211

How to cite

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Choquet-Bruhat, Yvonne, Christodoulou, Demetrios, and Francaviglia, Mauro. "Cauchy data on a manifold." Annales de l'I.H.P. Physique théorique 29.3 (1978): 241-255. <http://eudml.org/doc/76005>.

@article{Choquet1978,
author = {Choquet-Bruhat, Yvonne, Christodoulou, Demetrios, Francaviglia, Mauro},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {three dimensional manifold; Cauchy problem; general relativity; unique solution; weak differentiability; positive definite riemannian metric; Sobolev space; covariant derivative},
language = {eng},
number = {3},
pages = {241-255},
publisher = {Gauthier-Villars},
title = {Cauchy data on a manifold},
url = {http://eudml.org/doc/76005},
volume = {29},
year = {1978},
}

TY - JOUR
AU - Choquet-Bruhat, Yvonne
AU - Christodoulou, Demetrios
AU - Francaviglia, Mauro
TI - Cauchy data on a manifold
JO - Annales de l'I.H.P. Physique théorique
PY - 1978
PB - Gauthier-Villars
VL - 29
IS - 3
SP - 241
EP - 255
LA - eng
KW - three dimensional manifold; Cauchy problem; general relativity; unique solution; weak differentiability; positive definite riemannian metric; Sobolev space; covariant derivative
UR - http://eudml.org/doc/76005
ER -

References

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  1. [1] T. Aubin, Espaces de Sobolev sur les variétés riemaniennes. Bull. Sc. Math., 2e série, t. 100, 1976, p. 149-173. Zbl0328.46030MR488125
  2. [2] Y. Choquet-Bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. Acta Math., t. 88, 1952, p. 141-225. Zbl0049.19201MR53338
  3. [3] Y. Choquet-Bruhat, Espaces-temps einsteiniens généraux, chocs gravitationnels. Ann. Inst. H. Poincaré, t. 8, 1968, p. 327-338 (cf. also, C. R. Acad. Sci., Paris, t. 248, 1959). Zbl0162.29703MR233576
  4. [4] P. Dionne, Sur les problèmes de Cauchy bien posés. J. Anal. Math. Jerusalem, t. 10, 1962, p. 1-90. Zbl0112.32301MR150475
  5. [5] A. Fisher and J. Marsden, The Einstein evolution equations as a first order symmetric hyperbolic quasilinear system. Comm. Math. Phys., t. 28, 1972, p. 1-38. Zbl0247.35082MR309507
  6. [6] L. Garding, Cauchy's problem for hyperbolic equations. Lecture Notes (Chicago), 1957. Zbl0091.26902
  7. [7] S. Hawking and G. Ellis, The large structure of space-time. Cambridge University Press, Cambridge, 1973. Zbl0265.53054MR424186
  8. [8] T. Hughes, T. Kato and J. Marsden, Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity. Arch. Rat. Mech. and Anal., t. 63, 1976, p. 273-294. Zbl0361.35046MR420024
  9. [9] J. Leray, Hyperbolic differential equations (Institute for Advanced Study (Notes)), 1953. MR80849
  10. [10] A. Lichnerowicz, Propagateurs et commutateurs en relativité générale. Publ. Scient. I. H. E. S., t. 10, 1961, p. 293-344. Zbl0098.42607MR158726
  11. [11] S.L. Sobolev, Quelques questions de la théorie des équations aux dérivées partielles non linéaires. C. I. M. E., Varenna, 1956. 

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