Local uniqueness for an inverse boundary value problem with partial data
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- by Bastian Harrach and Marcel Ullrich PDF
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Abstract:
In dimension $n\geq 3$, we prove a local uniqueness result for the potentials $q$ of the Schrödinger equation $-\Delta u+qu=0$ from partial boundary data. More precisely, we show that potentials $q_1,q_2\in L^\infty$ with positive essential infima can be distinguished by local boundary data if there is a neighborhood of a boundary part where $q_1\geq q_2$ and $q_1\not \equiv q_2$.References
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Additional Information
- Bastian Harrach
- Affiliation: Department of Mathematics - IMNG, Chair of Optimization and Inverse Problems, University of Stuttgart, Allmandring 5b, 70569 Stuttgart, Germany
- Address at time of publication: Institute of Mathematics, Goethe University Frankfurt, Robert-Mayer-Str. 10, 60325 Frankfurt am Main, Germany
- Email: harrach@math.uni-frankfurt.de
- Marcel Ullrich
- Affiliation: Department of Mathematics - IMNG, University of Stuttgart, 70569 Stuttgart, Germany
- MR Author ID: 1042925
- Email: marcelullrich@gmx.de
- Received by editor(s): February 4, 2015
- Published electronically: November 28, 2016
- Additional Notes: The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart
- Communicated by: Joachim Krieger
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1087-1095
- MSC (2010): Primary 35J10; Secondary 35R30
- DOI: https://doi.org/10.1090/proc/12991
- MathSciNet review: 3589309