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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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1569-3945
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Volume 16, Issue 1

Issues

Recovering a potential from Cauchy data in the two-dimensional case

A. L. Bukhgeim
  • Wichita State University, Department of Mathematics and Statistics, 1845 N. Fairmount, Wichita, KS, 67260-0033, USA; Sobolev Institute of Mathematics, Koptyug prosp. 4, Novosibirsk, 630090, Russia. Email:
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Published Online: 2008-03-05 | DOI: https://doi.org/10.1515/jiip.2008.002

In this paper we prove that the Cauchy data for the Schrödinger equation in the two-dimensional case determines a potential from Lp (for p > 2) uniquely. We also obtain a linear inversion formula for smooth potentials.

Keywords: Riemann–Hilbert problem; potential; Schrödinger equation; inversion formula; Cauchy data

About the article

Received: 2007-06-14

Revised: 2007-11-24

Published Online: 2008-03-05

Published in Print: 2008-01-01


Citation Information: Journal of Inverse and Ill-posed Problems jiip, Volume 16, Issue 1, Pages 19–33, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2008.002.

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