In this paper we study the inverse boundary value problem of determining the potential in the Schrödinger 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.
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; Maarten V., De Hoop; Lingyun, Qiu. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - ELETTRONICO. - 45:2(2013), pp. 679-699. [10.1137/120869201]
LIPSCHITZ STABILITY OF AN INVERSE BOUNDARY VALUE PROBLEM FOR A SCHRODINGER-TYPE EQUATION
BERETTA, Elena;
2013
Abstract
In this paper we study the inverse boundary value problem of determining the potential in the Schrödinger 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
