Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map
Journal
Inverse Problems and Imaging
Journal Volume
Vol 8 (2014)
Pages
1139-1150
Date Issued
2014
Date
2014
Author(s)
Isakov, Victor
Abstract
We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schrödinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when energy level/frequency is growing. These boundshold under certain a-priori regularity constraints on the unknown coefficient. Proofs use complex and bounded complex geometrical optics solutions.
SDGs
Type
journal article