Recovery of singularities for formally determined inverse problems |
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Authors: | Ziqi Sun Gunther Uhlmann |
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Institution: | (1) Department of Mathematics and Statistics, Wichita State University, 67208 Wichita, Kansas, USA;(2) Department of Mathematics, University of Washington, 98195 Seattle, Washington, USA |
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Abstract: | In this paper we considered several formally determined problems in two dimensions. There are no global identifiability results for these problems. However, we can recover an important feature of these functions, namely their singularities. More precisely, we prove that one can determine the location and strength of singularities of anL
compactly supported potential by knowing the associated scattering amplitude at a fixed energy. Also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium.Partially supported by NSF grant DMS-9123742Partially supported by NSF grant DMS-9100178 |
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