Tuesday, February 14, 2012

1202.2829 (Oleg Imanuvilov et al.)

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

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

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