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2012

The massive wave equation in asymptotically AdS spacetimes

Warnick, C. M.

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We consider the massive wave equation on asymptotically AdS spaces.

We show that the timelike scri behaves like a finite timelike boundary, on which one may impose the equivalent of Dirichlet, Neumann or Robin conditions for a range of (negative) mass parameter which includes the conformally coupled case.
We demonstrate well posedness for the associated initial-boundary value problems at the $H^1$ level of regularity.
We also prove that higher regularity may be obtained, together with an asymptotic expansion for the field near scri.

The massive wave equation in asymptotically AdS spacetimes · Around

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Then

A. Bachelot, “The Dirac System on the Anti-de Sitter Universe,Ó Commun. Math. Phys. 283
2008
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L. C. Evans, “Partial Differential Equations,” Graduate Studies in Mathematics 19, AMS, Providence RI, 2008
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A. Vasy, “The wave equation on asymptotically Anti-de Sitter spaces,” to appear in Analysis and PDE (2009) arXiv:0911.5440
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