1202.2829 (Oleg Imanuvilov et al.)

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

Oleg Imanuvilov, Masahiro Yamamoto

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.

View original: http://arxiv.org/abs/1202.2829