Local uniqueness for an inverse boundary value problem with partial data

Bastian Harrach; Marcel Ullrich

doi:10.1090/proc/12991

paper

Local uniqueness for an inverse boundary value problem with partial data

arXiv:1810.05834 · doi:10.1090/proc/12991

Abstract

In dimension $n \geq 3$ , we prove a local uniqueness result for the potentials $q$ of the Schrödinger equation $- Δ u + q u = 0$ from partial boundary data. More precisely, we show that potentials $q_{1}, q_{2} \in L^{\infty}$ with positive essential infima can be distinguished by local boundary data if there is a neighborhood of a boundary part where $q_{1} \geq q_{2}$ and $q_{1} \neq \equiv q_{2}$ .