Geometric Analysis of Hyperbolic Differential Equations: an Introduction

Name: Geometric Analysis of Hyperbolic Differential Equations: an Introduction
Price: 67.6 USD
Availability: InStock
ISBN: 9780521128223

ISBN-10: 0521128226

ISBN-13: 9780521128223

Edition: 2010

Authors: S. Alinhac

List price: $78.95

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Book details

List price: $78.95
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



Preface



Introduction



Metrics and frames



Metrics, duality



Optical functions



Null frames



Computing with frames



Metric connection



Submanifolds



Hessian and d'Alembertian



Frame coefficients



Energy inequalities and frames



The energy-momentum teasor



Deformation teasor



Energy inequality formalism



Energy



Interior teems and positive fields



Maxwell equations



Duality



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


References


Index