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A generalization of the propagation of singularities theorem on asymptotically anti‐de Sitter spacetimes

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  • Claudio Dappiaggi
  • Alessio Marta

Abstract

In a recent paper O. Gannot and M. Wrochna considered the Klein–Gordon equation on an asymptotically anti‐de Sitter spacetime subject to Robin boundary conditions, proving in particular a propagation of singularities theorem. In this work we generalize their result considering a more general class of boundary conditions implemented on the conformal boundary via pseudodifferential operators of suitable order. Using techniques proper of b‐calculus and of twisted Sobolev spaces, we prove also for the case in hand a propagation of singularity theorem along generalized broken bicharacteristics, highlighting the potential presence of a contribution due to the pseudodifferential operator encoding the boundary condition.

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  • Claudio Dappiaggi & Alessio Marta, 2022. "A generalization of the propagation of singularities theorem on asymptotically anti‐de Sitter spacetimes," Mathematische Nachrichten, Wiley Blackwell, vol. 295(10), pages 1934-1968, October.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:10:p:1934-1968
    DOI: 10.1002/mana.202000287
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    References listed on IDEAS

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    1. Bernd Ammann & Nadine Große & Victor Nistor, 2019. "Well‐posedness of the Laplacian on manifolds with boundary and bounded geometry," Mathematische Nachrichten, Wiley Blackwell, vol. 292(6), pages 1213-1237, June.
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