Carleman commutator approach in logarithmic convexity for parabolic equations

Kim Dang Phung (1)

1 IDP - Institut Denis Poisson

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.

Domaines: Equations aux dérivées partielles [math.AP]

Kim Dang Phung. Carleman commutator approach in logarithmic convexity for parabolic equations. 2018. ⟨hal-01710168⟩