A weighted identity for partial differential operators of second order and its applications

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Null controllability of the complex Ginzburg-Landau equation Contrôlabilité à zéro de l'équation de Ginzburg-Landau complexe (2009, background): “Finally, [9] contains a Carleman inequality for the operator (a+ ib)∂t + ∑ j,k ∂k(a ∂j ) (where (a) is a smooth uniformly elliptic matrix) and a zero-controllability result for a linear PDE of GL type with an internal control.”
Carleman estimates for parabolic equations and applications (2009, background): “For other types of equations, such pointwise Carleman estimates were proved in [112] and see also [5, 59, 105, 145].”
Exact boundary controllability of the nonlinear Schrödinger equation (2009, background): “the Korteweg–de Vries equation (see [7,22,24, 25,29,31]), or the Ginzburg–Landau equation (see [6,26]).”
A unified controllability/observability theory for some stochastic and deterministic partial differential equations (2010, methodology): “Also, as pointed by [13], starting from Theorem 3.”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, background): “• Recently an unified approach for Carleman inequalities for parabolic and hyperbolic equations has been presented in [71].”