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Geometric Analysis of Hyperbolic Differential Equations: an Introduction

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ISBN-10: 0521128226

ISBN-13: 9780521128223

Edition: 2010

Authors: S. Alinhac

List price: $43.95
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Book details

List price: $43.95
Copyright year: 2010
Publisher: Cambridge University Press
Publication date: 5/20/2010
Binding: Paperback
Pages: 130
Size: 5.98" wide x 9.02" long x 0.28" tall
Weight: 0.418
Language: English

Metrics and frames
Metrics, duality
Optical functions
Null frames
Computing with frames
Metric connection
Hessian and d'Alembertian
Frame coefficients
Energy inequalities and frames
The energy-momentum teasor
Deformation teasor
Energy inequality formalism
Interior teems and positive fields
Maxwell equations
Energy formalism
The good components
The problem
An important remark
Ghost weights and improved standard energy inequalities
Conformal inequalities
Pointwise estimates and commutations
Pointwise decay and conformal inqualities
Commuting fields in the scalar case
Modified Lorentz fields
Commuting fields for Maxwell equaticus
Frames and curvature
The curvature tensor
Optical functions and curvature
Transport equations
Elliptic systems
Mixed transport-elliptic systems
Nonlinear equations, a priori estimates and induction
A simple ODE example
Local existence theory
Blowup criteria
Induction on time for PDFs
Applications to some quasilinear hyperbolic problems
Quasilnear wave equations satisfying the null condition
Quasilinear wave equations
Low regularity well-posedness for quasilinear wave equations
Stability of Minkowski spacetime (first version)
L<sup>2</sup> conjecture on the curvature
Stability of Minkowsld spacetime (second version)
The formation of black holes