Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity
Analysis of PDEs
2021-05-28 v1
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.
Keywords
Cite
@article{arxiv.2105.12977,
title = {Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity},
author = {Rémi Buffe and Kim Dang Phung},
journal= {arXiv preprint arXiv:2105.12977},
year = {2021}
}