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Partial data inverse problems for the Hodge Laplacian

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Chung, F. J., Salo, M., & Tzou, L. (2017). Partial data inverse problems for the Hodge Laplacian. Analysis and PDE, 10(1), 43-93. https://doi.org/10.2140/apde.2017.10.43
Published in
Analysis and PDE
Authors
Chung, Francis J. |
Salo, Mikko |
Tzou, Leo
Date
2017
Discipline
MatematiikkaMathematics
Copyright
© the Authors, 2017. Published in this repository with the kind permission of the publisher.

 
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.
Publisher
Mathematical Sciences Publishers
ISSN Search the Publication Forum
2157-5045
Keywords
Hodge Laplacian partial data absolute and relative boundary conditions admissible manifolds Carleman estimates inversio-ongelmat
DOI
https://doi.org/10.2140/apde.2017.10.43
URI

http://urn.fi/URN:NBN:fi:jyu-201801121165

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/26894714

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