Abstract
The authors prove global existence of small solutions to a semilinear wave equation outside of convex obstacles. This extends results of Christodoulou and Klainerman who handled the Minkowski space version. The proof is a compromise of the methods of Christodoulou and Klainerman. It relies on local estimates proved earlier by Smith and Sogge together with classical energy decay estimates for the wave equation of Morawetz, Lax and Phillips.
Original language | English (US) |
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Pages (from-to) | 805-842 |
Number of pages | 38 |
Journal | American Journal of Mathematics |
Volume | 122 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2000 |