Abstract
In this paper we study the inverse boundary value problem of determining the potential in the Schrodinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz-type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values.
Original language | English (US) |
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Pages (from-to) | 679-699 |
Number of pages | 21 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 45 |
Issue number | 2 |
DOIs | |
State | Published - 2013 |
Keywords
- Helmholtz equation
- Inverse boundary value problem
- Lipschitz stability
- Schrodinger equation
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics