On the null-controllability of diffusion equations

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On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, background): “Some recent results are available with some lower bonds and uperbounds [47,57].”
Time optimal boundary controls for the heat equation (2012, methodology): “Our methodology is partially inspired by the fact, remarked in Tenenbaum and Tucsnak [23], that a well-known inequality of Turán can be successfully used in control theory.”