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Carleman estimates for the Schrödinger operator and applications to unique continuation

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  • We extend previously known Carleman estimates [18, 16, 11] for the (time-dependent) Schrödinger operator $i\partial_t+\Delta$ to a wider range for which inhomogeneous Strichartz estimates ([9, 27]) are known to hold. Then we apply them to obtain new results on unique continuation for the Schrödinger equation which include more general classes of potentials. Also, we obtain a unique continuation result for nonlinear Schrödinger equations.
    Mathematics Subject Classification: Primary: 35B45, 35B60; Secondary: 35Q40, 35Q55.

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