On the stability of an inverse problem in potential theory (Q1090448)

The authors consider the problem of finding the density of a material body when the strength of the gravitational field on its surface is known. The continuous dependence of the solution upon datum in \(L^ 2\)- metrics (i.e., stability) is proved for those densities in a neighborhood of any regular positive solution for which the (harmonic) perturbation term has a bounded gradient.