Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map

Victor Isakov

doi:10.3934/dcdss.2011.4.631

Article Contents

2011, Volume 4, Issue 3: 631-640. Doi: 10.3934/dcdss.2011.4.631

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Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map

Victor Isakov^1,

1.
Wichita State University, 1845 Fairmount, Wichita, KS, 67260-0033

Received: April 2009

Revised: September 2009

Published: June 2011

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Abstract

We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovery of the potential coefficient in the Schrödinger equation from the Dirichlet-to-Neumann map, when frequency (energy level) is growing. These bounds hold under certain a-priori bounds on the unknown coefficient. Proofs use complex- and real-valued geometrical optics solutions. We outline open problems and possible future developments.

Keywords:

Inverse Problems,
Inverse Scattering.

Mathematics Subject Classification: Primary: 35R30; Secondary: 78A46.

Citation:

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