| Abstract: |
| Inverse boundary value problems
need strong a priori assumptions to ensure a good rate of stability. We consider the inverse conductivity problem in the case of piecewise constant conductivities defined on a known partition of the domain. While the general problem is severely ill-posed, exhibiting logarithmic stability, the introduction of structural a priori information allows for stronger stability results.
We prove Lipschitz stability of the map from the conductivity to the Dirichlet-to-Neumann operator within this class. The analysis relies on the finite-dimensional structure of the parameter space together with quantitative unique continuation and propagation of smallness arguments. |
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