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An Introduction
Serge Alinhac
ISBN: 9780521128223
Format: Paperback
Publisher:Cambridge University Press
Also available as an eBook
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Its self-contained presentation and "do-it-yourself" approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of non-linear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics…
Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.
| ISBN | 0521128226 | | Weight (grammes) | 190 | | ISBN13 | 9780521128223
(What's this?) | | Published in | Cambridge | | Publisher | Cambridge University Press | | Series ISSN | 0076-055 | | Imprint | Cambridge University Press | | Series title | London Mathematical Society Lecture Note Series | | Format | Paperback | | Height (mm) | 228 | | Publication date | 20 May 2010 | | Width (mm) | 152 | | DEWEY | 515.3535 | | Spine width (mm) | 8 | | DEWEY edition | DC22 | | Academic level | Professional / Scholarly | | Pages | 128 | |
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| | | Preface | | | | 1 | | Introduction | | 1 | | 2 | | Metrics and frames | | 8 | | 2.1 | | Metrics, duality | | 8 | | 2.2 | | Optical functions | | 12 | | 2.3 | | Null frames | | 12 | | 3 | | Computing with frames | | 17 | | 3.1 | | Metric connexion | | 17 | | 3.2 | | Submanifolds | | 20 | | 3.3 | | Hessian and d'Alembertian | | 21 | | 3.4 | | Frame coefficients | | 24 | | 4 | | Energy inequalities and frames | | 29 | | 4.1 | | The energy-momentum tensor | | 29 | | 4.2 | | Deformation tensor | | 31 | | 4.3 | | Energy inequality formalism | | 33 | | 4.4 | | Energy | | 34 | | 4.5 | | Interior terms and positive fields | | 35 | | 4.6 | | Maxwell equations | | 41 | | 4.6.1 | | Duality | | 41 | | 4.6.2 | | Energy formalism | | 43 | | 5 | | The good components | | 45 | | 5.1 | | The problem | | 45 | | 5.2 | | An important remark | | 46 | | 5.3 | | Ghost weights and improved standard energy inequalities | | 47 | | 5.4 | | Conformal inequalities | | 53 | | 6 | | Pointwise estimates and commutations | | 57 | | 6.1 | | Pointwise decay and conformal inequalities | | 58 | | 6.2 | | Commuting fields in the scalar case | | 59 | | | More... | | |
'This book provides an excellent introduction to nonlinear wave equations, and it can be recommended to anyone who wants to access the recent mathematical literature on this subject.' Zentralblatt MATH  Be the first to write a customer review
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