Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limit

Abstract

We consider the partial data inverse boundary problem for the Schrödinger operator at a frequency $k>0$ on a bounded domain in ${\mathbb{R}}^n$, $n\ge 3$, with impedance boundary conditions. Assuming that the potential is known in a neighborhood of the boundary, we first show that the knowledge of the partial Robin-to-Dirichlet map at the fixed frequency $k>0$ along an arbitrarily small portion of the boundary, determines the potential in a logarithmically stable way. We prove, as the principal result of this work, that the logarithmic stability can be improved to the one of Hölder type in the high frequency regime.