Endpoint Strichartz estimates for the Schrödinger equation on an exterior domain

Abstract: The purpose in this paper is to prove end point Strichartz estimates for the Schr\"odinger equation in the exterior domain of a generic non-trapping obstacle in the case $n \geq 3.$ In the case $n=2$ we have the same range of Strichartz estimates as in the free case. In this version we corrected some misprints from the previous one.