|
| On the Main Aspects of the Inverse Conductivity Problem |
| |
| View Full Text View/Add Comment Download reader |
| KeyWord:Calder{\'o}n problem Inverse conductivity problem Dirichlet-to-Neumann map Complex geometrical optics solutions Carleman estimate |
|
| Hits: 414 |
| Download times: 599 |
| Abstract: |
| We consider a nonlinear inverse problem for an elliptic partial differential equation known as the Calder{\'o}n 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 Schr\"odinger 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. |
|
|
|
