Geometric Analysis of Hyperbolic Differential Equations

An Introduction
Erscheinungsjahr 2015
ISBN: 978-0-521-12822-3
Verlag: Cambridge University Press

Buch, Englisch, Band 374, 128 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 201 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Alinhac, S.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Preface
1. Introduction
2. Metrics and frames
3. Computing with frames
4. Energy inequalities and frames
5. The good components
6. Pointwise estimates and commutations
7. Frames and curvature
8. Nonlinear equations, a priori estimates and induction
9. Applications to some quasilinear hyperbolic problems
References
Index.

Über Autor(innen)

Alinhac, S.
S. Alinhac is Professor in the Department of Mathematics at the University of Paris-Sud 11, Orsay.