Instability in the Gel'fand inverse problem at high energies

TL;DR

This paper provides an instability estimate for the Gel'fand inverse boundary value problem at high energies, demonstrating the limits of stability in such inverse problems.

Contribution

It establishes an optimality result for the stability estimates in the Gel'fand inverse problem at high energies.

Findings

Shows the instability estimate is optimal.

Highlights limitations of stability in high-energy inverse problems.

Connects to prior stability results, confirming their optimality.

Abstract

We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.