Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 267, Issue 4, Pages 2471-2502Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2019.03.019
Keywords
Maxwell system; Inverse boundary problem; Identifiability and uniqueness; Electroencephalography and magnetoencephalography
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Funding
- NSF grant of China [11601528]
- NSF grant of Hunan [2017JJ3432, 2018JJ3622]
- Innovation-Driven Project of Central South University [2018CX041]
- Mathematics and Interdisciplinary Sciences Project of Central South University
- Hong Kong Baptist University
- Hong Kong RGC General Research Funds [12302415, 12302017, 12301218]
- NSF
- IAS, HKUST
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We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively. (C) 2019 Published by Elsevier Inc.
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