Weak wave operators for the nonlinear wave equation

Abstract

In [2] and [3], Strauss studied this problem when q has sufficiently rapid decay at infinity. In this paper we will derive some information for the case q -1. The basic parts used will be the energy estimates of Strauss derived in [2] and an elementary lemma about Hilbert spaces. While the results in this paper refer to the existence of wave operators in the weak topology, they open new methods of attacking the problem in the strong topology.