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
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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MR2473363
Choquet-Bruhat, Yvonne
General relativity and the Einstein equations.
Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009.