Abstract
On the basis of the Carleman estimate for the parabolic equation, we prove a Carleman estimate for the integro-differential operator $$\partial _t-\triangle +\int _0^t K(x,t,r)\triangle \ dr$$ where the integral kernel has a behaviour like a weakly singular one. In the proof we consider the integral term as a perturbation. The crucial point is a special choice of the time factor of the weight function.
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