Unique continuation from infinity in asympotically Anti-de Sitter spacetimes II: Non-static boundaries
| Autor: | Gustav Holzegel, Arick Shao |
|---|---|
| Přispěvatelé: | Commission of the European Communities |
| Rok vydání: | 2016 |
| Předmět: |
Class (set theory)
media_common.quotation_subject General Mathematics Mathematics Applied Boundary (topology) FOS: Physical sciences Conformal map General Relativity and Quantum Cosmology (gr-qc) 83C99 (General Relativity) 01 natural sciences General Relativity and Quantum Cosmology 0101 Pure Mathematics symbols.namesake Continuation Mathematics - Analysis of PDEs 0102 Applied Mathematics 0103 physical sciences FOS: Mathematics 0101 mathematics 35L05 (Partial Differential Equations) Klein–Gordon equation Mathematics Mathematical physics media_common Science & Technology 010308 nuclear & particles physics Applied Mathematics 010102 general mathematics Infinity Carleman estimates unique continuation Anti de Sitter Nonlinear system 35A02 35Q75 83C30 35L05 Physical Sciences symbols Klein-Gordon equation Anti-de Sitter space Analysis Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1608.07521 |
| Popis: | We generalize our unique continuation results recently established for a class of linear and nonlinear wave equations $\Box_g \phi + \sigma \phi = \mathcal{G} ( \phi, \partial \phi )$ on asymptotically anti-de Sitter (aAdS) spacetimes to aAdS spacetimes admitting non-static 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 pseudoconvex hypersurfaces near the conformal boundary. Comment: 45 pages. Newest version incorporated changes from referee comments and fixed minor typos |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|