Abstract
We study some properties of weighted Sobolev spaces with asymptotic conditions appropriate to physical conditions on non compact space times. An existence and uniqueness theorem of non compact maximal space-like hypersurfaces for asymptotically flat metrics in a neighbourhood of the Minkowski's metric is proved.
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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, 485–491 (1977). https://doi.org/10.1007/BF00399740
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DOI: https://doi.org/10.1007/BF00399740