Soichiro Katayama, Hideo Kubo
Published 2007-06-13, updated 2007-07-04Version 2
The aim of this article is to present an elementary proof of a global existence result for nonlinear wave equations satifying the null condition in an exterior domain. The novelty of our proof is to avoid completely the scaling operator which would make the argument complicated in the mixed problem, by using a new weighted pointwise estimates of a tangential derivative to the light cone.
Comments: (i) To simplify the proof of Theorems 4.1 and 4.2 in the previous version, we added Lemma 4.1. (ii) Proof of the theorem for general situation of the multiple speeds are given, while it was proved only for the single speed case in the previous version. (iii) (3.2) is replaced by its accurate form. (iv) Some refernces are added, and many typos are corrected
Journal: J. Math. Soc. Japan. 60 (2008) 1135-1170
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