Energy Scattering for Nonlinear Klein-Gordon and Schrödinger Equations in Spatial Dimensions 1 and 2

Abstract

We show that when n=1 and 2, the scattering operators are well-defined in the whole energy space for nonlinear Klein-Gordon and Schrödinger equations in R1+n with nonlinearity up-1u, p>1+4/n. Such results have been known only for n≥3. © 1999 Academic Press.