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Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity

Abstract : We prove an inequality of Hölder type traducing the unique continuation property at one time for the heat equation with a potential and Neumann boundary condition. The main feature of the proof is to overcome the propagation of smallness by a global approach using a refined parabolic frequency function method. It relies with a Carleman commutator estimate to obtain the logarithmic convexity property of the frequency function.
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https://hal.archives-ouvertes.fr/hal-03238278
Contributor : Rémi Buffe <>
Submitted on : Thursday, May 27, 2021 - 8:52:13 AM
Last modification on : Friday, May 28, 2021 - 3:35:02 AM

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  • HAL Id : hal-03238278, version 1

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Rémi Buffe, Kim Dang Phung. Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity. 2021. ⟨hal-03238278⟩

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