A singular initial-boundary value problem for nonlinear wave equations and holography in asymptotically anti-de Sitter spaces

摘要

We analyze the initial value problem for semilinear Klein-Gordon equations on asymptotically anti-de Sitter spaces using energy methods adapted to the geometry of the problem at infinity. The key feature is that the coefficients become strongly singular at infinity, which leads to considering nontrivial data on the conformal boundary of the manifold. This question arises in Physics as the holographic prescription problem in string theory. (C) 2014 Elsevier Masson SAS. All rights reserved.