Double Logarithmic Stability in the Identification of a Scalar Potential by a Partial Elliptic Dirichlet-to-Neumann Map
We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schrödinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data is imposed on the shadowed face of the boundary of the domain and the Neumann data is measured on its illuminated face. We establish a log log stability estimate for the L2-norm (resp. the H-1-norm) of Ht, for t>0, and bounded (resp. L2) potentials.