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.
Cite this article
Matthias Günther, Über zwei spezielle inverse Probleme der Potentialtheorie. Z. Anal. Anwend. 6 (1987), no. 5, pp. 459–470DOI 10.4171/ZAA/264