On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

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Controllability of Two Coupled Wave Equations on a Compact Manifold (2013, unknown): “As (1 − ) 1 2 w0 1 is an eigenfunction of the Laplace operator vanishing on O, a unique continuation result (see for instance the classical reference [6,7], the book [47] or the exposition article [25]) yields (1 − ) 1 2 w0 1 = 0 on .”
Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations (2015, background): “h ∈ L2((0,T) × (0,1)), supported in a subset ωof [0,1], such that the solution uof (1.1) satisﬁes u(T,x) = 0 for all x∈ [0,1] (see, for instance, [1] - [6], [13] - [19], [26], [27], [30], [31], [33], [40], [41], [42], [47] and the references therein). Moreover, Carleman estimates are also extremely ”
On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems (2014, background): “Steps 2 and 3 of the proof are standard and have been recalled for readability convenience, see for instance [35] or ([50], Appendix IV).”
Null controllability of Grushin-type operators in dimension two (2011, background): “For the proof of Proposition 8 we shall need the following inequality obtained in [32] (see also [33]).”
Observability Inequalities and Measurable Sets (2012, background): “4) has been proved under condition that ∂Ω is at least C(2) [28, 29, 41, 32].”