Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements

Abstract

We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This estimate is proved under the assumption that the potential is known near the boundary of a domain when the dimension is greater than or equal to $3$. In addition, we show a triple logarithmic stability for an interior impedance problem.