Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
Analysis of PDEs
2015-06-04 v1 Mathematical Physics
math.MP
Abstract
We consider an inverse problem of determining coefficient matrices in an -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.
Cite
@article{arxiv.1202.2829,
title = {Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations},
author = {Oleg Imanuvilov and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:1202.2829},
year = {2015}
}