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

A. L. Bukhgeim

doi:10.1515/jiip.2008.002

Published by De Gruyter March 5, 2008

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

A. L. Bukhgeim

From the journal Journal of Inverse and Ill-posed Problems

https://doi.org/10.1515/jiip.2008.002

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In this paper we prove that the Cauchy data for the Schrödinger equation in the two-dimensional case determines a potential from L_p (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

Received: 2007-June-14

Revised: 2007-November-24

Published Online: 2008-03-05

Published in Print: 2008-01

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

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