Imperial College London
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ProfessorGustavHolzegel

Faculty of Natural Sciences, Department of Mathematics

Professor of Pure Mathematics
 
 
 
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g.holzegel CV

 
 
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Location

 

625Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Holzegel:2019:10.1007/s00220-019-03601-6,
author = {Holzegel, G and Luk, J and Smulevici, J and Warnick, C},
doi = {10.1007/s00220-019-03601-6},
journal = {Communications in Mathematical Physics},
pages = {1125--1178},
title = {Asymptotic properties of linear field equations in anti-de sitter space},
url = {http://dx.doi.org/10.1007/s00220-019-03601-6},
volume = {374},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We study the global dynamics of the wave equation, Maxwell’s equation and the linearized Bianchi equations on a fixed anti-de Sitter (AdS) background. Provided dissipative boundary conditions are imposed on the dynamical fields we prove uniform boundedness of the natural energy as well as both degenerate (near the AdS boundary) and non-degenerate integrated decay estimates. Remarkably, the non-degenerate estimates “lose a derivative”. We relate this loss to a trapping phenomenon near the AdS boundary, which itself originates from the properties of (approximately) gliding rays near the boundary. Using the Gaussian beam approximation we prove that non-degenerate energy decay without loss of derivatives does not hold. As a consequence of the non-degenerate integrated decay estimates, we also obtain pointwise-in-time decay estimates for the energy. Our paper provides the key estimates for a proof of the non-linear stability of the anti-de Sitter spacetime under dissipative boundary conditions. Finally, we contrast our results with the case of reflecting boundary conditions.
AU  - Holzegel,G
AU  - Luk,J
AU  - Smulevici,J
AU  - Warnick,C
DO  - 10.1007/s00220-019-03601-6
EP  - 1178
PY  - 2019///
SN  - 0010-3616
SP  - 1125
TI  - Asymptotic properties of linear field equations in anti-de sitter space
T2  - Communications in Mathematical Physics
UR  - http://dx.doi.org/10.1007/s00220-019-03601-6
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000493950500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00220-019-03601-6
UR  - http://hdl.handle.net/10044/1/75110
VL  - 374
ER  -
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