Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity

Details Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity Strichartz estimates for Schrödinger equations with variable coefficients and potentials at most linear at spatial infinity

2011-08-10

arxiv.org/abs/1108.2103v2

Mathematics

Analysis of PDEs

24pages

Scientific paper

In the present paper we consider Schr\"odinger equations with variable coefficients and potentials, where the principal part is a long-range perturbation of the flat Laplacian and potentials have at most linear growth at spatial infinity. We then prove local-in-time Strichartz estimates, outside a large compact set centered at origin, expect for the endpoint. Moreover we also prove global-in-space Strichartz estimates under the non-trapping condition on the Hamilton flow generated by the kinetic energy.

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