In this paper, densities that give solution to the Cauchy problem for the Laplace equation in an annular region two-dimensional are calculated in exact form when techniques of the potential theory are used for finding such solution. This is important since these exact densities allow validating algorithms given for solving the problem, but even more, they are important in themselves since they can provide important information about the processes carried out on the boundaries. In particular, the density associated with the double layer potential (defined on boundary of the annular region) can provide information about the bioelectrical activity on the cerebral cortex associated with the group of pyramidal neurons.

inverse problem, potential theory, bioelectrical source, regularization methods.