Über zwei spezielle inverse Probleme der Potentialtheorie

Abstract

The problem to determine the shape of a solid body is treated if the density and the values of its Newtonian potential or the gradient of the latter on the surface are known. The considerations have a local character, i.e. the unknown body is situated in a neighbourhood of a known initial configuration. In the existence proofs the inverse function theorem is used as well as estimations for potentials of variable domains.