Strichartz Estimates for Schrödinger Equations with Variable Coefficients

Details Strichartz Estimates for Schrödinger Equations with Variable Coefficients Strichartz Estimates for Schrödinger Equations with Variable Coefficients

2005-01-20

arxiv.org/abs/math/0501319v1

Mathematics

Analysis of PDEs

193 pages

Scientific paper

We prove the (local in time) Strichartz estimates (for the full range of parameters given by the scaling unless the end point) for asymptotically flat and non trapping perturbations of the flat Laplacian in $\R^n$, $n\geq 2$. The main point of the proof, namely the dispersion estimate, is obtained in constructing a parametrix. The main tool for this construction is the use of the FBI transform.

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