Increasing stability of the inverse boundary value problem for the Schrödinger equation. (English) Zbl 1330.35531
Stefanov, Plamen (ed.) et al., Inverse problems and applications. Proceedings of two conferences in honour of Gunther Uhlmann’s 60th birthday, Irvine, CA, USA, June 18–22, 2012 and Hangzhou, China, September 17–21, 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1079-7/pbk; 978-1-4704-1659-1/ebook). Contemporary Mathematics 615, 131-141 (2014).
Summary: In this work, we study the phenomenon of increasing stability in the inverse boundary value problem for the Schrödinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of the wave number (or energy). The main contribution of this work is to provide a unified and easier approach to the same problem based on the complex geometrical optics solutions.
For the entire collection see [Zbl 1290.35005].
For the entire collection see [Zbl 1290.35005].
MSC:
| 35R30 | Inverse problems for PDEs |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 35B35 | Stability in context of PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 78A05 | Geometric optics |
