Geometric Analysis of Hyperbolic Differential Equations
S. Alinhac
Bok Engelsk 2010 · Electronic books.
| Annen tittel | |
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| Utgitt | Cambridge : Cambridge University Press , 2010
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| Omfang | 1 online resource (130 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Title; Copyright; Contents; Preface; 1 Introduction; 2 Metrics and frames; 2.1 Metrics, duality; 2.2 Optical functions; 2.3 Null frames; 3 Computing with frames; 3.1 Metric connexion; 3.2 Submanifolds; 3.3 Hessian and d'Alembertian; 3.4 Frame coefficients; 4 Energy inequalities and frames; 4.1 The energy-momentum tensor; 4.2 Deformation tensor; 4.3 Energy inequality formalism; 4.4 Energy; 4.5 Interior terms and positive fields; 4.6 Maxwell equations; 4.6.1 Duality; 4.6.2 Energy formalism; 5 The good components; 5.1 The problem; 5.2 An important remark. - 5.3 Ghost weights and improved standard energy inequalities5.4 Conformal inequalities; 6 Pointwise estimates and commutations; 6.1 Pointwise decay and conformal inequalities; 6.2 Commuting fields in the scalar case; 6.3 Modified Lorentz fields; 6.4 Commuting fields for Maxwell equations; 7 Frames and curvature; 7.1 The curvature tensor; 7.2 Optical functions and curvature; 7.3 Transport equations; 7.4 Elliptic systems; 7.5 Mixed transport-elliptic systems; 8 Nonlinear equations, a priori estimates and induction; 8.1 A simple ODE example; 8.2 Local existence theory; 8.3 Blowup criteria. - 8.4 Induction on time for PDEs9 Applications to some quasilinear hyperbolic problems; 9.1 Quasilinear wave equations satisfying the null condition; 9.2 Quasilinear wave equations; 9.3 Low regularity well-posedness for quasilinear wave equations; 9.4 Stability of Minkowski spacetime (first version); 9.5 L2 conjecture on the curvature; 9.6 Stability of Minkowski spacetime (second version); 9.7 The formation of black holes; References; Index. - A self-contained presentation of the tools of Lorentzian geometry necessary to access recent works in mathematical relativity.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9780521128223
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