Geodesic
Control for Schrödinger operators on 2-tori: rough potentials
Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1597-1628.

Voir la notice de l'article provenant de la source EMS Press

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)
DOI : 10.4171/jems/399
Classification : 00-XX
Keywords: 
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     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/}
}
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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. http://geodesic.mathdoc.fr/articles/10.4171/jems/399/

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