Local logarithmic stability of an inverse coefficient problem for a singular heat equation with an inverse-square potential

An inverse problem of the determination of the coefficient P(x) in the equation: partial derivative(t)u(x, t)- del . (P(x)del u) - mu/vertical bar x vertical bar(2) u(x, t) = 0, (x, t) is an element of Omega x (0, T) is considered. The main difficulty here as compared with the existing result is that there is a singular potential in the equation. A local logarithmic stability estimate is obtained using the method of Carleman estimates. Our proof relies on the Bukhgeim-Klibanov method which was originated in [Bukhgeim AL, Klibanov MV. Uniqueness in the large of a class of multidi-imensional inverse problems. Dokl Akad Nauk SSSR. 1981;17:244-247] to prove inverse source or coefficient results.