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Partial data inverse
problems for the Hodge Laplacian
Francis J. Chung, Mikko Salo and Leo Tzou |
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Vol. 10 (2017), No. 1, 43–93
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Abstract |
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We prove uniqueness results for a Calderón-type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth-order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometrical optics solutions which reduce the Calderón-type problem to a tomography problem for 2-tensors. The arguments in this paper allow us to establish partial data results for elliptic systems that generalize the scalar results due to Kenig, Sjöstrand and Uhlmann. |
Keywords
inverse problems, Hodge Laplacian, partial data, absolute
and relative boundary conditions, admissible manifolds,
Carleman estimates
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Mathematical Subject Classification 2010
Primary: 35R30
Secondary: 58J32
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Milestones
Received: 9 March 2016
Revised: 10 May 2016
Accepted: 19 September 2016
Published: 30 January 2017
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Authors |
| Francis J. Chung | |
| Department of Mathematics University of Kentucky Lexington, KY 40506 United States |
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| Mikko Salo | |
| Department of Mathematics and
Statistics University of Jyväskylä FI-40014 Jyväskylä Finland |
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| Leo Tzou | |
| School of Mathematics and
Statistics University of Sydney Sydney NSW 2006 Australia |
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