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The Calderón problem
for the fractional Schrödinger equation
Tuhin Ghosh, Mikko Salo and Gunther Uhlmann |
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Vol. 13 (2020), No. 2, 455–475
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Abstract |
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We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calderón problem. |
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Keywords
inverse problem, Calderón problem, fractional Laplacian,
approximation property
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Mathematical Subject Classification 2010
Primary: 26A33, 35J10, 35R30
Secondary: 35J70
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Milestones
Received: 9 July 2018
Revised: 8 November 2018
Accepted: 23 February 2019
Published: 19 March 2020
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Authors |
| Tuhin Ghosh | |
| Jockey Club Institute for Advanced
Study Hong Kong University of Science and Technology Kowloon Hong Kong |
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| Mikko Salo | |
| Department of Mathematics and
Statistics University of Jyväskylä Jyväskylä Finland |
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| Gunther Uhlmann | |
| Department of Mathematics University of Washington Seattle, WA United States |
Jockey Club Institute for Advanced
Study Hong Kong University of Science and Technology Kowloon Hong Kong |
