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.
LIPSCHITZ STABILITY OF AN INVERSE BOUNDARY VALUE PROBLEM FOR A SCHRODINGER-TYPE EQUATION
BERETTA, ELENA;
2013-01-01
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.File in questo prodotto:
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