The inverse Robin boundary value problem in a half-space

Abstract

We study the inverse Robin problem for the Schrödinger equation in a half-space. The potential differing from a constant is assumed to be compactly supported. We first solve the direct problem for dimensions two and three. We then show that the Robin-to-Robin map uniquely determines the potential .

Keywords:

• inverse problems
• Schrödinger equation
• impedance parameter
• Robin-to-Robin map

AMS Subject Classifications:

• 35G15
• 35J10
• 35R30
• 35Q60

Acknowledgement

The authors would like to express their gratitude to Katya Krupchyk for helpful and useful comments on the paper.