Rough controls for Schroedinger operators on 2-tori
Analysis of PDEs
2017-12-27 v1 Optimization and Control
Abstract
The purpose of this note is to use the results and methods of our previous work with Bourgain to obtain control and observability by rough functions and sets on rectangular 2-tori. We show that any Lebesgue measurable set of positive measure can be used for observability for the Schroedinger equation. This leads to controllability with rough localization and control functions. For non-empty open sets this follows from the results of Haraux '89 and Jaffard '89 while for square tori and sufficiently long times this can be deduced from the results of Jakobson '97.
Keywords
Cite
@article{arxiv.1712.08635,
title = {Rough controls for Schroedinger operators on 2-tori},
author = {Nicolas Burq and Maciej Zworski},
journal= {arXiv preprint arXiv:1712.08635},
year = {2017}
}