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

2013/10/01 by Alberto Enciso, Niky Kamran, Enciso, Alberto +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1310.0158

41 pages

openalex publication_date 2013/10/01 · arxiv created 2013/10/14 · arxiv updated 2013/10/15 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We analyze the initial value problem for semilinear wave 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.

Cited by

• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography

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