Instability in the Gel'fand inverse problem at high energies

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 preceding stability results on inverse problems of such a type.

Keywords:

• inverse boundary value problems
• Dirichlet-to-Neumann map
• stability estimates

AMS Subject Classification:

• 35R30

Acknowledgements

This work was fulfilled in the framework of research carried out under the supervision of R.G. Novikov.