Increasing stability for determining the potential in the Schrodinger equation with attenuation from the Dirichlet-to-Neumann map
Isakov, Victor Wang, Jenn-Nan
Isakov, Victor
Wang, Jenn-Nan
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2014-11
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Article
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Inverse problems,Schrodinger operator,Quantum mechanics,Fundamental solutions,Perturbation theories
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Isakov, Victor, 1947-; Wang, Jenn-Nan. 2014. Increasing stability for determining the potential in the Schrodinger equation with attenuation from the Dirichlet-to-Neumann map. Inverse Problems and Imaging (IPI), vol. 8:no. 4:pp 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 Schrodinger 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.
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American Institute of Mathemaical Sciences
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Inverse Problems and Imaging
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1930-8337