Stability for the inverse potential problem by the local Dirichlet-to-Neumann map for the Schrödinger equation

Abstract

In this article we study, in dimension n ≥ 3, the inverse problem of determining the potential q of the Schrödinger equation from infinity measurements on any open subset Γ₀ of the boundary. Provided that q is known in a neighborhood of the boundary, we prove the logarithmic stability estimate.

Keywords:

• Dirichlet--Neumann map
• Inverse problems
• Schrödinger equation
• 2000 Mathematics Subject Classifications
• 35R25
• 35R30

Acknowledgement

Many thanks is due to professor Mourad Bellassoued for inspiring question, fruitful discussions and for his careful reading of the manuscript.