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Unique continuation from infinity in asymptotically anti-de Sitter spacetimes II: Non-static boundaries

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Title: Unique continuation from infinity in asymptotically anti-de Sitter spacetimes II: Non-static boundaries
Authors: Holzegel, G
Shao, A
Item Type: Journal Article
Abstract: We generalize our unique continuation results recently established for a class of linear and nonlinear wave equations □gϕ+σϕ = (ϕ,∂ϕ) on asymptotically anti-de Sitter (aAdS) spacetimes to aAdS spacetimes admitting nonstatic boundary metrics. The new Carleman estimates established in this setting constitute an essential ingredient in proving unique continuation results for the full nonlinear Einstein equations, which will be addressed in forthcoming papers. Key to the proof is a new geometrically adapted construction of foliations of pseudo-convex hypersurfaces near the conformal boundary.
Issue Date: 27-Nov-2017
Date of Acceptance: 19-Sep-2017
URI: http://hdl.handle.net/10044/1/51803
DOI: https://dx.doi.org/10.1080/03605302.2017.1390677
ISSN: 0360-5302
Publisher: Taylor & Francis
Start Page: 1871
End Page: 1922
Journal / Book Title: Communications in Partial Differential Equations
Volume: 42
Issue: 12
Copyright Statement: © 2017 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Partial Differential Equations on 27 November 2017, available online: http://www.tandfonline.com/doi/abs/10.1080/03605302.2017.1390677
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: FP7-ERC-2013-StG-337488
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Anti de Sitter
Carleman estimates
Klein-Gordon equation
unique continuation
35L05 (Partial Differential Equations)
83C99 (General Relativity)
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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