Cauchy problem seminar, Sommersemester 2011

Some references for the wave equation on Minkowski space-time:

Taylor, Michael E.
Partial differential equations I. Basic theory.
Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011.

Copson, E. T.
Partial differential equations.
Cambridge University Press, Cambridge-New York-Melbourne, 1975.

Evans, Lawrence C.
Partial differential equations.
Second edition. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010.

The spherical means approach, etc.: pp. 75-95 from Evans's PDEs I, or from Copson

Fourier methods for the Minkowski wave equation: Taylor part I Taylor part II

On Sonya Kovalevskaya (djvu)

Here are scans of the Ehlers-Friedrich-Rendall-Schmidt notes on the Cauchy problem, Garching preprint "Das Cauchy Problem", 1989:
p4 p14 p1-p19.pdf p20-p26.pdf p27-p42.pdf p43-p56.pdf

The Lewy example

Link to the Lewy paper

Matthias Koeck notes on the Lewy example

Cauchy problem in GR

My lecture notes on the Cauchy problem

Further reading:

The Cauchy problem for the Einstein equations.
Helmut Friedrich, Alan D. Rendall AEI-2000-012. Feb 2000. 97 pp.
Published in Lect.Notes Phys. 540 (2000) 127-224
e-Print: gr-qc/0002074

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Ringström, Hans
The Cauchy problem in general relativity.
ESI Lectures in Mathematics and Physics. European Mathematical Society (EMS), Zürich, 2009.

The Constraint equations.
Robert Bartnik (Canberra U.), Jim Isenberg (Oregon U.). 2002. 34 pp.
To appear in the proceedings of SPIRES Conference C02/07/29.1 (Conference information coming soon)
e-Print: gr-qc/0405092

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Choquet-Bruhat, Yvonne
General relativity and the Einstein equations.
Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009.