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arXiv · 2105.12977

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

Rémi Buffe·Kim Dang Phung
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Abstract

We prove an inequality of H\"older 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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Rémi Buffe, Kim Dang Phung. 2021-05-27. Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity. https://arxiv.org/abs/2105.12977

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