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 conditions. 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 on a Carleman commutator estimate to obtain the logarithmic convexity property of the frequency function.
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Acknowledgements
The authors thank Hoai–Minh Nguyen for fruitful discussions about this work. No datasets were generated or analyzed during the current work, and the authors declare no conflict of interest.
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Buffe, R., Phung, K.D. Observation estimate for the heat equations with Neumann boundary conditions via logarithmic convexity. J. Evol. Equ. 22, 86 (2022). https://doi.org/10.1007/s00028-022-00842-2
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DOI: https://doi.org/10.1007/s00028-022-00842-2