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2009, Volume 23, Issue 1&2: 341-365. Doi: 10.3934/dcds.2009.23.341
This issue Previous Article Interaction of boundary layers and corner singularities Next Article A Carleman estimate for the linear shallow shell equation and an inverse source problem

Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity

  • 1.

    Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris

  • 2.

    Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Universite Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris

  • 3.

    Institüt für Mathematik, Abt. Angewandte Mathematik, Universitüt Zürich, Winterthurerstrasse 190, 8057 Zürich

Received:  October 31, 2007
Revised:  December 31, 2007
Published:  April 2009
Abstract Related Papers Cited by
    Abstract
  • Assuming minimal regularity assumptions on the data, we revisit the classical problem of findingisometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold.Our approach encompasses metrics having Sobolev regularity and Riemann curvature definedin the distributional sense, only.It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature that possibly changesfrom point to point.
    Mathematics Subject Classification: Primary: 53C50, 83C99; Secondary: 51B20, 57Q35, 14J70.

    Citation:
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