Observability estimate for the parabolic equations with inverse square potential

This paper investigates an observability estimate for the parabolic equations with inverse square potential in a C-2 bounded domain Omega subset of R-d, which contains 0. The observation region is a product set of a subset E subset of (0, T] with positive measure and a non-empty open subset omega subset of Omega with 0 is not an element of omega. We build up this estimate by a delicate result in measure theory in [7] and the Lebeau-Robbiano strategy.