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

DOI10.1016/j.matpur.2014.10.005zbMath1406.35203arXiv1310.0158OpenAlexW2964205820MaRDI QIDQ1756300

Alberto Enciso, Niky Kamran

Publication date: 14 January 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.0158

zbMATH Keywords

nonlinear wavesCauchy problemAdS/CFT correspondencesemilinear Klein-Gordon equations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Hyperbolic equations on manifolds (58J45) Higher-order semilinear hyperbolic equations (35L76) Singular hyperbolic equations (35L81)

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Determining an asymptotically AdS Einstein spacetime from data on its conformal boundary ⋮ Fractional powers of the wave operator via Dirichlet-to-Neumann maps in anti-de Sitter spaces ⋮ On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary ⋮ Unique continuation from infinity in asymptotically anti-de Sitter spacetimes ⋮ The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes ⋮ A generalization of the propagation of singularities theorem on asymptotically anti‐de Sitter spacetimes ⋮ Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetimes ⋮ Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes ⋮ The near-boundary geometry of Einstein-vacuum asymptotically anti-de Sitter spacetimes ⋮ Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials ⋮ PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION

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