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 Schr\"odinger equation. The rigorous justification of increasing stability for the IBVP for Schr\"odinger equation were established by Isakov Isa11 and by Isakov, Nagayasu, Uhlmann, Wang of the paper INUW14. In Isa11, 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 H\"older type. In this work, we prove that the instability changes from an exponential type to a H\"older type when the frequency increases. This result verifies that results in Isa11, INUW14 are optimal.
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