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

Vladimir Georgiev; Koichi Taniguchi

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

Analysis of PDEs 2024-04-11 v3

Authors: Vladimir Georgiev , Koichi Taniguchi

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.

Keywords

endpoint strichartz estimates schrödinger equation exterior domain non-trapping obstacle free case

Cite

@article{arxiv.1905.02483,
  title  = {Endpoint Strichartz estimates for the Schr\"odinger equation on an exterior domain},
  author = {Vladimir Georgiev and Koichi Taniguchi},
  journal= {arXiv preprint arXiv:1905.02483},
  year   = {2024}
}

Comments

We found an essential gap in the proof of the main result

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