Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map
Open Access
- 1 January 2014
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Inverse Problems and Imaging
- Vol. 8 (4) , 1139-1150
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 bounds hold under certain a-priori regularity constraints on the unknown coefficient. Proofs use complex and bounded complex geometrical optics solutions.Keywords
All Related Versions
This publication has 19 references indexed in Scilit:
- Energy and regularity dependent stability estimates for the Gel'fand inverse problem in multidimensionsJournal of Inverse and Ill-posed Problems, 2012
- Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann mapDiscrete and Continuous Dynamical Systems - S, 2011
- Recovering a potential from Cauchy data in the two-dimensional caseJournal of Inverse and Ill-posed Problems, 2008
- Inverse scattering by a continuation method with initial guesses from a direct imaging algorithmJournal of Computational Physics, 2007
- Increased stability in the continuation for the Helmholtz equation with variable coefficient2007
- Stable Determination of an Inclusion by Boundary MeasurementsSIAM Journal on Mathematical Analysis, 2005
- Increased stability in the continuation of solutions to the Helmholtz equationInverse Problems, 2004
- Stability of recovering the near-field wave from the scattering amplitudeInverse Problems, 1996
- A Periodic Faddeev-Type Solution OperatorJournal of Differential Equations, 1996
- Stable determination of conductivity by boundary measurementsApplicable Analysis, 1988