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Well-posedness for the massive wave equation on asymptotically anti-de Sitter spacetimes

Mar, 2011
23 pages
Published in:
  • J.Hyperbol.Diff.Equat. 9 (2012) 02, 239-261
  • Published: May 31, 2012
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Abstract: (WSP)
In this paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner–Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class (but non-unique if the decay at infinity is weakened).
  • Asymptotically AdS spacetimes
  • Klein–Gordon equation
  • Breitenlohner–Freedman bound