Carleman Estimates with No Lower-Order Terms for General Riemann Wave Equations. Global Uniqueness and Observability in One Shot

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Uniform stabilization of the damped Cauchy–Ventcel problem with variable coefficients and dynamic boundary conditions (2007, methodology): “46), and subsequently invoking ellipticity and the Uniqueness Continuation theorem of Triggiani and Yao [20], as was done in the final part of Case I, we arrive at (ũt , ṽt ) = (0,0) and (ũ, ṽ) = (0,0), a conclusion which contradicts (5.”
Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carleman estimates. Part I: H 1(Ω)-estimates (2004, methodology): “case; [46] for ¢g as principal part; also focused on the Neumann B.”
Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge (2017, background): “rticular, this proves Theorem 1.4. 8. The foliation condition and corollaries The assumption of an existence of a strictly convex function appears also in some works on Carleman estimates, see, e.g., [32] and the references there. Existence of such a function is also assumed in the recent work [18] ”
Asymptotic Stability of the Wave Equation on Compact Manifolds and Locally Distributed Damping: A Sharp Result (2010, background): “In addition, because of the radially symmetric region (Fig. 5), we are not sure if the uniqueness results due to Triggiani and Yao [ 30 ] can be employed to our case, so that new unique continuation arguments are required (see Theorem 5.1).”