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Local uniqueness for an inverse boundary value problem with partial data


Authors: Bastian Harrach and Marcel Ullrich
Journal: Proc. Amer. Math. Soc. 145 (2017), 1087-1095
MSC (2010): Primary 35J10; Secondary 35R30
DOI: https://doi.org/10.1090/proc/12991
Published electronically: November 28, 2016
MathSciNet review: 3589309
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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$.


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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
Email: marcelullrich@gmx.de

DOI: https://doi.org/10.1090/proc/12991
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
Article copyright: © Copyright 2016 American Mathematical Society