Stability for the inverse potential problem by finite measurements on the boundary

In this paper, we investigate the inverse problem of determining the potential of the Schrodinger equation from finite measurements on the boundary. It is well known that this is an ill posed problem in the sense of Hadamard. The stability estimate is proved under the assumption that the potentials have some a priori constraints. Based on this conditional stability result, we propose one kind of Tikhonov regularization and prove the convergence rate for the regularized solution.