Mittag-Leffler’s function and extracting from Cauchy data

We give an application of Mittag-Leffler’s function to the inverse conductivity problem. We establish a formula for extracting information about the location and shape of an unknown inclusion from the Dirichlet-to-Neumann map. The method is a generalization of the enclosure method introduced by the author himself and yields much information more than the convex hull of the unknown inclusion. A regularization of the formula is also described.

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