TY - JOUR
T1 - On the Main Aspects of the Inverse Conductivity Problem
AU - Aoudj , Manal
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 1
EP - 17
PY - 2022
DA - 2022/06
SN - 4
DO - http://doi.org/10.12150/jnma.2022.1
UR - https://global-sci.org/intro/article_detail/jnma/20690.html
KW - Calderόn problem, Inverse conductivity problem, Dirichlet-to-Neumann map, Complex geometrical optics solutions, Carleman estimate.
AB - <p style="text-align: justify;">We consider a nonlinear inverse problem for an elliptic partial differential equation known as the Calderόn problem or the inverse conductivity
problem. Based on several results, we briefly summarize them to motivate
this research field. We give a general view of the problem by reviewing the
available results for $C^2$ conductivities. After reducing the original problem to
the inverse problem for a Schrödinger equation, we apply complex geometrical optics solutions to show its uniqueness. After extending the ideas of the
uniqueness proof result, we establish a stable dependence between the conductivity and the boundary measurements. By using the Carleman estimate,
we discuss the partial data problem, which deals with measurements that are
taken only in a part of the boundary.</p>