Strichartz estimates for long range perturbations

Details Strichartz estimates for long range perturbations Strichartz estimates for long range perturbations

2005-09-21

arxiv.org/abs/math/0509489v2

Mathematics

Analysis of PDEs

to appear in American Journal of Mathematics

Scientific paper

We study local in time Strichartz estimates for the Schroedinger equation associated to long range perturbations of the flat Laplacian on the euclidean space. We prove that in such a geometric situation, outside of a large ball centered at the origin, the solutions of the Schroedinger equation enjoy the same Strichartz estimates as in the non perturbed situation. The proof is based on the Isozaki-Kitada parametrix construction. If in addition the metric is non trapping, we prove that the Strichartz estimates hold in the whole space.

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