Inverse medium problem for a singular contrast

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Serov , V & Tyni , T 2019 , ' Inverse medium problem for a singular contrast ' , Journal of Mathematical Physics , vol. 60 , no. 11 , 111508 .

Title: Inverse medium problem for a singular contrast
Author: Serov, V.; Tyni, T.
Contributor organization: Department of Mathematics and Statistics
Inverse Problems
Date: 2019-11
Language: eng
Number of pages: 15
Belongs to series: Journal of Mathematical Physics
ISSN: 0022-2488
Abstract: We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.
111 Mathematics
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: publishedVersion

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