Scattering Theory in the Energy Space for a Class of Hartree Equations

Details Scattering Theory in the Energy Space for a Class of Hartree Equations Scattering Theory in the Energy Space for a Class of Hartree Equations

1998-09-30

arxiv.org/abs/math/9809183v1

Mathematics

Analysis of PDEs

TeX, 41 pages, available http://qcd.th.u-psud.fr

Scientific paper

We study the theory of scattering in the energy space for the Hartree equation in space dimension n>2. Using the method of Morawetz and Strauss, we prove in particular asymptotic completeness for radial nonnegative nonincreasing potentials satisfying suitable regularity properties at the origin and suitable decay properties at infinity. The results cover in particular the case of the potential |x|^(- gamma) for 2 < gamma < Min(4,n).

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