Control for Schrödinger operators on 2-tori: rough potentials
Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1597-1628
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For the Schrödinger equation, (i∂t+Δ)u=0 on a torus, an arbitrary non-empty open set Ω provides control and observability of the solution: ∥u∣t=0∥L2(T2)≤KT∥u∥L2([0,T]×Ω) . We show that the same result remains true for (i∂t+Δ−V)u=0 where V∈L2(T2) , and T2 is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for V∈C(T2) and conjectured for V∈L∞(T2) . The higher dimensional generalization remains open for V∈L∞(Tn)
@article{JEMS_2013_15_5_a1,
author = {Jean Bourgain and Nicolas Burq and Maciej Zworski},
title = {Control for {Schr\"odinger} operators on 2-tori: rough potentials},
journal = {Journal of the European Mathematical Society},
pages = {1597--1628},
publisher = {mathdoc},
volume = {15},
number = {5},
year = {2013},
doi = {10.4171/jems/399},
url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/399/}
}
TY - JOUR AU - Jean Bourgain AU - Nicolas Burq AU - Maciej Zworski TI - Control for Schrödinger operators on 2-tori: rough potentials JO - Journal of the European Mathematical Society PY - 2013 SP - 1597 EP - 1628 VL - 15 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4171/jems/399/ DO - 10.4171/jems/399 ID - JEMS_2013_15_5_a1 ER -
%0 Journal Article %A Jean Bourgain %A Nicolas Burq %A Maciej Zworski %T Control for Schrödinger operators on 2-tori: rough potentials %J Journal of the European Mathematical Society %D 2013 %P 1597-1628 %V 15 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4171/jems/399/ %R 10.4171/jems/399 %F JEMS_2013_15_5_a1
Jean Bourgain; Nicolas Burq; Maciej Zworski. Control for Schrödinger operators on 2-tori: rough potentials. Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1597-1628. doi: 10.4171/jems/399
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