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

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

2012-02-13

arxiv.org/abs/1202.2829v1

Mathematics

Analysis of PDEs

Scientific paper

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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