Partial Differential Equations
Inverse problem for the Schrödinger operator in an unbounded strip
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 635-640.

We prove an adapted global Carleman estimate and an energy estimate for the Schrödinger operator H:=it+(c) in an unbounded strip. Using these estimates, we give a stability result for the diffusion coefficient c(x,y) from the measurement of the normal derivative of the solution on a part of the boundary.

Nous démontrons une estimation globale de Carleman et une estimation d'énergie pour l'opérateur de Schrödinger H:=it+(c) dans une bande non bornée. Ces estimations nous permettent de donner un résultat de stabilité pour le coefficient de diffusion c(x,y) à partir de la mesure de la dérivée normale de la solution sur une partie du bord.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.04.004
Cardoulis, Laure 1; Cristofol, Michel 2; Gaitan, Patricia 2

1 CEREMATH/UMR MIP, Université de Toulouse 1, 21, allées de Brienne, 31000 Toulouse, France
2 Laboratoire d'Analyse Topologie Probabilités, CNRS UMR 6632, Universités d'Aix-Marseille, 13453 Marseille cedex, France
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Cardoulis, Laure; Cristofol, Michel; Gaitan, Patricia. Inverse problem for the Schrödinger operator in an unbounded strip. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 635-640. doi : 10.1016/j.crma.2008.04.004. http://www.numdam.org/articles/10.1016/j.crma.2008.04.004/

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