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Zeitschrift für Analysis und ihre Anwendungen

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Volume 6, Issue 5, 1987, pp. 459–470
DOI: 10.4171/ZAA/264

Published online: 1987-10-31

Über zwei spezielle inverse Probleme der Potentialtheorie

Matthias Günther[1]

(1) Universität Leipzig, Germany

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.

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Günther Matthias: Über zwei spezielle inverse Probleme der Potentialtheorie. Z. Anal. Anwend. 6 (1987), 459-470. doi: 10.4171/ZAA/264