Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data

Abstract

To show increasing stability in the problem of recovering potential $c \in C^1(\Omega)$ in the Schrödinger equation with the given partial Cauchy data when energy frequency $k$ is growing, we will obtain some bounds for $c$ which can be viewed as an evidence of such phenomenon. The proof uses almost exponential solutions and methods of reflection.