]. A. Bdl07a, Y. Benabdallah, J. L. Dermenjian, and . Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem, J. Math. Anal. Appl, vol.336, pp.865-887, 2007.

]. A. Bdl07b, Y. Benabdallah, J. L. Dermenjian, and . Rousseau, On the controllability of linear parabolic equations with an arbitrary control location for stratified media, C. R. Acad. Sci. Paris, Ser I, vol.344, pp.357-362, 2007.

Y. [. Benabdallah, J. L. Dermenjian, and . Rousseau, Carleman estimates for stratified media, Journal of Functional Analysis, vol.260, issue.12, pp.3645-3677, 2011.
DOI : 10.1016/j.jfa.2011.02.007

URL : https://hal.archives-ouvertes.fr/hal-00529924

M. Bellassoued, Carleman estimates and distribution of resonances for the transparent obstacle and application to the stabilization, Asymptotic Anal, vol.35, pp.257-279, 2003.

A. Benabdallah, P. Gaitan, and J. L. Rousseau, Stability of Discontinuous Diffusion Coefficients and Initial Conditions in an Inverse Problem for the Heat Equation, SIAM Journal on Control and Optimization, vol.46, issue.5, pp.1849-1881, 2007.
DOI : 10.1137/050640047

URL : https://hal.archives-ouvertes.fr/hal-00016490

]. H. Bre83 and . Brezis, Analyse Fonctionnelle, 1983.

]. N. Bur98 and . Burq, Décroissance de l'´ energie locale de l'´ equation des ondes pour leprobì eme extérieur et absence de résonance au voisinage du réel, Acta Math, vol.180, issue.1, pp.1-29, 1998.

A. [. Doubova, J. Osses, and . Puel, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.621-661, 2002.
DOI : 10.1051/cocv:2002047

J. [. Grigis and . Sjöstrand, Microlocal Analysis for Differential Operators, 1994.
DOI : 10.1017/CBO9780511721441

]. L. Hör63 and . Hörmander, Linear Partial Differential Operators, 1963.

]. L. Hör79 and . Hörmander, The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math, vol.32, pp.359-443, 1979.

]. L. Hör85a and . Hörmander, The Analysis of Linear Partial Differential Operators, volume III, 1985.

L. Hörmanderhör90-]-l and . Hörmander, The Analysis of Linear Partial Differential Operators, volume IV The Analysis of Linear Partial Differential Operators, volume I, 1985.

D. Jerison and G. Lebeau, Harmonic analysis and partial differential equations (Chicago, IL, 1996), chapter Nodal sets of sums of eigenfunctions, Chicago Lectures in Mathematics, pp.223-239, 1999.