The Calderón Problem with Partial Data for Conductivities with 3/2 Derivatives

We extend a global uniqueness result for the Calderón problem with partial data, due to Kenig–Sjöstrand–Uhlmann (Ann. Math. (2) 165:567–591, 2007 ), to the case of less regular conductivities. Specifically, we show that in dimensions n ≥ 3 , the knowledge of the Diricihlet-to-Neumann map, measured o...

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Bibliographic Details
Published in:Communications in mathematical physics 2016-11, Vol.348 (1), p.185-219
Main Authors: Krupchyk, Katya, Uhlmann, Gunther
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Conductivity
Derivatives
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Uniqueness
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Summary:We extend a global uniqueness result for the Calderón problem with partial data, due to Kenig–Sjöstrand–Uhlmann (Ann. Math. (2) 165:567–591, 2007 ), to the case of less regular conductivities. Specifically, we show that in dimensions n ≥ 3 , the knowledge of the Diricihlet-to-Neumann map, measured on possibly very small subsets of the boundary, determines uniquely a conductivity having essentially 3/2 derivatives in an L 2 sense.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2666-z