JournalsjemsVol. 21, No. 11pp. 3513–3572

Observability and unique continuation inequalities for the Schrödinger equation

  • Gengsheng Wang

    Tianjin University, China

  • Ming Wang

    China University of Geosciences, Wuhan, China

  • Yubiao Zhang

    Tianjin University, China
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Abstract

We present several observability and unique continuation inequalities for the free Schrödinger equation in the whole space. The observations in these inequalities are made either at two points in time or one point in time. These inequalities correspond to different kinds of controllability for the free Schrödinger equation. We also show that the observability inequality at two points in time is equivalent to the uncertainty principle given in [21].

Cite this article

Gengsheng Wang, Ming Wang, Yubiao Zhang, Observability and unique continuation inequalities for the Schrödinger equation. J. Eur. Math. Soc. 21 (2019), no. 11, pp. 3513–3572

DOI 10.4171/JEMS/908