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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Inverse scattering for singular potentials in two dimensions


Authors: Zi Qi Sun and Gunther Uhlmann
Journal: Trans. Amer. Math. Soc. 338 (1993), 363-374
MSC: Primary 35P25; Secondary 35J10, 35R30
MathSciNet review: 1126214
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Abstract: We consider the Schrödinger equation for a compactly supported potential having jump type singularities at a subdomain of $ {\mathbb{R}^2}$. We prove that knowledge of the scattering amplitude at a fixed energy, determines the location of the singularity as well as the jump across the curve of discontinuity. This result follows from a similar result for the Dirichlet to Neumann map associated to the Schrödinger equation for a compactly supported potential with the same type of singularities.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1126214-4
PII: S 0002-9947(1993)1126214-4
Article copyright: © Copyright 1993 American Mathematical Society