Optimality of increasing stability for an inverse boundary value problem

Abstract

In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schrödinger equation. The rigorous justification of increasing stability for the IBVP for Schrödinger equation were established by Isakov \cite{Isa11} and by Isakov, Nagayasu, Uhlmann, Wang of the paper \cite{INUW14}. In \cite{Isa11}, \cite{INUW14}, the authors showed that the stability of this IBVP increases as the frequency increases in the sense that the stability estimate changes from a logarithmic type to a Hölder type. In this work, we prove that the instability changes from an exponential type to a Hölder type when the frequency increases. This result verifies that results in \cite{Isa11}, \cite{INUW14} are optimal.

Cited by in corpus (3)

• The Calderón problem for the fractional wave equation: Uniqueness and optimal stability
• The Born approximation for the fixed energy Calderón problem
• Increasing stability of the first order linearized inverse Schrödinger potential problem with integer power type nonlinearities