Unique continuation for the Schr\"odinger equation with gradient term

Youngwoo Koh; Ihyeok Seo

Unique continuation for the Schr\"odinger equation with gradient term

Analysis of PDEs 2017-09-05 v3

Authors: Youngwoo Koh , Ihyeok Seo

Abstract

We obtain a unique continuation result for the differential inequality $| (i\partial_t +\Delta)u | \leq |Vu| + | W\cdot\nabla u |$ by establishing $L^2$ Carleman estimates. Here, $V$ is a scalar function and $W$ is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schr\"odinger equation.

Keywords

schrödinger equation

Cite

@article{arxiv.1603.06852,
  title  = {Unique continuation for the Schr\"odinger equation with gradient term},
  author = {Youngwoo Koh and Ihyeok Seo},
  journal= {arXiv preprint arXiv:1603.06852},
  year   = {2017}
}

Comments

To appear in Proc. Amer. Math. Soc., 8 pages

Related papers

View all related →