Acta Mathematica

, Volume 146, Issue 1, pp 129–150 | Cite as

Elliptic systems inH s,δ spaces on manifolds which are euclidean at infinity

  • Y. Choquet-bruhat
  • D. Christodoulou


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  1. [1]
    Bancel, D. &Lacaze, J., Spaces of Functions with Asymptotic Conditions and Existence of Non Compact Maximal submanifolds of a Lorentzian Manifold.Lett. Math. Phys., 1: 6 (1977), 485MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Cantor, M., Some problems of global analysis on asymptotically simple manifolds.Compositio Math., 38: 1 (1979), 3–35.MATHMathSciNetGoogle Scholar
  3. [3]
    —, A necessary and sufficient condition for York data to specify an asymptotically flat spacetime.J. Mathematical Phys., 20 (1979), 1741–1744.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Chaljub-Simon, A. &Choquet-Bruhat, Y., Problems elliptiques du second ordre sur une variete euclidienne a l'infini.Ann. Fac. Sci. Toulouse, 1 (1978), 9–25.MathSciNetGoogle Scholar
  5. [5]
    Choquet-Bruhat, Y., DeWitt-Morette, C. & Dillard-Bleick, M.,Analysis, manifolds and physics. North Holland (1977).Google Scholar
  6. [6]
    Choquet-Bruhat, Y. & York, J. W., Cauchy problem, inEinstein Centenary Volume. P. Bergman, J. Goldberg and A. Held editors (1979).Google Scholar
  7. [7]
    Douglis, A. &Nirenberg, L., Interior estimates for elliptic systems of partial differential equations.Comm. Pure Appl. Math., 3 (1955), 503–538.MathSciNetGoogle Scholar
  8. [8]
    Gilbarg, D. & Trudinger, N. S.,Elliptic partial differential equations of second order, Springer-Verlag (1977).Google Scholar
  9. [9]
    Gårding, L., Dirichlet's problem for linear elliptic partial differential equations.Math. Scand., 1 (1953), 55–72.MATHMathSciNetGoogle Scholar
  10. [10]
    John, F.,Plane waves and spherical means applied to partial differential equations. Interscience Publishers, New York (1955).MATHGoogle Scholar
  11. [11]
    Marsden, J.,Applications of global analysis in mathematical physics. Publish or Perish Inc., Boston Mass. (1974).MATHGoogle Scholar
  12. [12]
    McOwen, R. C., Behavior of the Laplacian on weighted Sobolev spaces,Comm. Pure Appl. Math., 32 (1979), 783–795.MATHMathSciNetGoogle Scholar
  13. [13]
    Morrey, C. B.,Multiple integrals in the calculus of variations. Springer-Verlag (1966).Google Scholar
  14. [14]
    Nirenberg, L. &Walker, H. F., The null spaces of elliptic partial differential operators inR n.J. Math. Anal. Appl., 42 (1973), 271–301.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Almqvist & Wiksell 1981

Authors and Affiliations

  • Y. Choquet-bruhat
    • 1
  • D. Christodoulou
    • 2
  1. 1.Department de MécaniqueUniversité de ParisFrance
  2. 2.Max-Planck-Institut für AstrophysikMünchenGermany

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