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Regularity results for semilinear and geometric wave equations. (English) Zbl 0895.35065
Chruściel, Piotr T. (ed.), Mathematics of gravitation. Part I: Lorentzian geometry and Einstein equations. Proceedings of the workshop on mathematical aspects of theories of gravitation, Warsaw, Poland, February 29–March 30, 1996. Warsaw: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 41(1), 69-90 (1997).
Cauchy problems for semilinear wave equations and for wave maps are considered. A survey on results together with ideas and techniques for the proofs are presented. For the semilinear wave equation particular attention is paid to critical cases and to optimal regularity results in Sobolev spaces. For wave maps additional blow-up results are discussed, depending on the target manifold.
For the entire collection see [Zbl 0880.00054].
Reviewer: R.Racke (Konstanz)

35L70 Second-order nonlinear hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
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