| Abstract: |
| We investigate the decay in the interior of solutions to elliptic equations with respect to the boundary data. In particular, the decay rate is linked to the so-called frequency of the boundary datum and is in general stronger when coefficients are smoother. We show applications of these decay results to the electrical impedance tomography.
A key ingredient in the proof is to study the distance function from the boundary for a Riemannian manifold. We show that, up to a conformal change of the metric, it coincides with the distance in the Euclidean case, thus inheriting its regularity properties. |
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