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arXiv · 1202.2829

Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations

Oleg Imanuvilov·Masahiro Yamamoto
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Abstract

We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is as follows: If two systems of elliptic operators generate the same set of partial Cauchy data on an arbitrary subboundary, then the coefficient matrices of the first-order and zero-order terms satisfy the prescribed system of first-order partial differential equations. The main result implies the uniqueness of any two coefficient matrices provided that the one remaining matrix among the three coefficient matrices is known.

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Oleg Imanuvilov, Masahiro Yamamoto. 2012-02-13. Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations. https://doi.org/10.1088/0266-5611%2F28%2F9%2F095015

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