[Inégalité d'observabilité pour les équations de Schrödinger stochastiques]
Dans cette Note, nous établissons une inégalité d'observabilité pour les équations de Schrödinger stochastiques avec des termes d'ordre inférieur à coefficients non réguliers. Notre inégalité s'obtient à partir des inégalités de Carleman globales qui découlent d'une identité à poids pour les opérateurs de type Schrödinger stochastiques. Comme conséquence intéressante de cette identité, on retrouve tous les résultats connus de controlabilité/observabilité pour les équations aux dérivées partielles stochastiques et déterministes, de type Schrödinger et hyperboliques, où l'utilisation des inégalités de Carleman a joué un rôle.
In this Note, we present an observability estimate for stochastic Schrödinger equations with nonsmooth lower order terms. The desired inequality is derived by a global Carleman estimate which is based on a fundamental weighted identity for stochastic Schrödinger-like operator. As an interesting byproduct, starting from this identity, one can deduce all the known controllability/observability results for several stochastic and deterministic partial differential equations that are derived before via Carleman estimate in the literature.
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@article{CRMATH_2010__348_21-22_1159_0,
author = {L\"u, Qi},
title = {Observability estimate for stochastic {Schr\"odinger} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1159--1162},
publisher = {Elsevier},
volume = {348},
number = {21-22},
year = {2010},
doi = {10.1016/j.crma.2010.10.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.10.016/}
}
TY - JOUR AU - Lü, Qi TI - Observability estimate for stochastic Schrödinger equations JO - Comptes Rendus. Mathématique PY - 2010 SP - 1159 EP - 1162 VL - 348 IS - 21-22 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.10.016/ DO - 10.1016/j.crma.2010.10.016 LA - en ID - CRMATH_2010__348_21-22_1159_0 ER -
%0 Journal Article %A Lü, Qi %T Observability estimate for stochastic Schrödinger equations %J Comptes Rendus. Mathématique %D 2010 %P 1159-1162 %V 348 %N 21-22 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.10.016/ %R 10.1016/j.crma.2010.10.016 %G en %F CRMATH_2010__348_21-22_1159_0
Lü, Qi. Observability estimate for stochastic Schrödinger equations. Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1159-1162. doi : 10.1016/j.crma.2010.10.016. http://www.numdam.org/articles/10.1016/j.crma.2010.10.016/
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