, Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations, http://hal.archives-ouvertes, Bur98] N. 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, pp.180-181, 1998.
, Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms, Journal of Optimization Theory and Applications, vol.45, issue.2, pp.245-264, 2001.
DOI : 10.1023/A:1017515027783
, Resolvent conditions for the controllability of parabolic semigroups, manuscript Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians Spectral asymptotics in the semi-classical limit Lectures on semiclassical analysis, Version 0, Cambridge Tracts in Mathematics Ema95] O. Yu. ` Emanuilov, Controllability of parabolic equations, pp.335-395, 1984.
, Some results on controllability for linear and nonlinear heat equations in unbounded domains, Adv. Differential Equations, vol.12, issue.11, pp.1201-1240, 2007.
, Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential, Journ??es ??quations aux d??riv??es partielles, vol.171, issue.2, pp.151-218, 2004.
DOI : 10.5802/jedp.606
, Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians, Lecture Notes in Mathematics, vol.1862, 2005.
DOI : 10.1007/b104762
, Nodal sets of sums of eigenfunctions, Harmonic analysis and partial differential equations, Univ. Chicago Press Tataru, L p eigenfunction bounds for the Hermite operator, Duke Math, pp.223-239, 1963.
, Contr??le Exact De L??quation De La Chaleur, Communications in Partial Differential Equations, vol.52, issue.1-2, pp.335-356, 1995.
DOI : 10.1016/0022-0396(87)90043-X
, Université de Provence -Aix-Marseille I. http://tel.archives-ouvertes.fr/tel-00201887 Introduction aux inégalités de Carleman pour les opérateurs elliptiques et paraboliques Carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations, Représentation microlocale de solutions de systèmes hyperboliques, 2007.
, Null-Controllability of a System of Linear Thermoelasticity, Archive for Rational Mechanics and Analysis, vol.141, issue.4, pp.297-329, 1998.
DOI : 10.1007/s002050050078
, Eigenfunctions for partially rectangular billiards, Comm. Partial Differential Equations, vol.31, pp.4-6, 2006.
, Controllability cost of conservative systems: resolvent condition and transmutation, J. Funct. Anal, vol.218, issue.2, pp.425-444, 2005.
, On the lack of null-controllability of the heat equation on the half-line, Transactions of the American Mathematical Society, vol.353, issue.04, pp.1635-1659, 2001.
DOI : 10.1090/S0002-9947-00-02665-9
, Exponential lower bounds for quasimodes of semiclassical Schrödinger operators, Math. Res. Lett, vol.16, issue.4, pp.721-734, 2009.
, Null controllability for the heat equation with singular inverse-square potentials, Journal of Functional Analysis, vol.254, issue.7, pp.1864-1902, 2008.
DOI : 10.1016/j.jfa.2007.12.015
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