# American Institute of Mathematical Sciences

September  2018, 8(3&4): 899-933. doi: 10.3934/mcrf.2018040

## Carleman commutator approach in logarithmic convexity for parabolic equations

 Institut Denis Poisson, CNRS, UMR 7013, Université d’Orléans, BP 6759, 45067 Orléans Cedex 2, France

Received  August 2017 Revised  December 2017 Published  September 2018

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

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.

Citation: Kim Dang Phung. Carleman commutator approach in logarithmic convexity for parabolic equations. Mathematical Control & Related Fields, 2018, 8 (3&4) : 899-933. doi: 10.3934/mcrf.2018040
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