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Carleman commutator approach in logarithmic convexity for parabolic equations

This work is supported by the Région Centre (France) - THESPEGE Project

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  • In this paper we investigate on a new strategy combining the logarithmic convexity (or frequency function) and the Carleman commutator to obtain an observation estimate at one time for the heat equation in a bounded domain. We also consider the heat equation with an inverse square potential. Moreover, a spectral inequality for the associated eigenvalue problem is derived.

    Mathematics Subject Classification: Primary: 35K05, 35K65; Secondary: 35B60, 35P20.


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