# Endpoint Strichartz estimates for the Schr\"odinger equation on an exterior domain

## TL;DR

This paper proves endpoint Strichartz estimates for the Schrödinger equation in exterior domains of non-trapping obstacles for dimensions three and higher, and confirms similar results as in free space for two dimensions.

## Contribution

It establishes endpoint Strichartz estimates for the Schrödinger equation in exterior domains, extending known results to non-trapping obstacles and correcting previous misprints.

## Key findings

- Endpoint estimates proven for n ≥ 3
- Results match free case for n=2
- Corrections made to previous version

## 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.