Stability estimates in inverse problem for potentials in system of two Schr¨odinger equations with Dirichlet and Neumann conditions

Abstract

We study the inverse problem on identifying two unknown potential coefficients in a system of coupled Schr¨odinger equations in a bounded domain in $\mathbb{R}^{n}$ subject to non--homogeneous Dirichlet and Neumann boundary conditions by using Neumann and Dirichlet boundary measurements. Under specific convexity assumptions on the geometry of domain and minimal regularity conditions on the data, we establish the Lipschitz stability of this inverse problem by employing uniqueness results as well as the observability inequality.