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 an arbitrary sub-boundary. The main result of this paper is as follows. If two systems of elliptic operators generate the same set of partial Cauchy data on an arbitrary sub-boundary, 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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