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Variational solutions of some nonlinear free boundary problems

✍ Scribed by J. F. G. Auchmuty; Richard Beals

Publisher: Springer
Year: 1971
Tongue: English
Weight: 763 KB
Volume: 43
Category: Article
ISSN: 0003-9527
DOI: 10.1007/bf00250465

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## Abstract In this paper we study some overdetermined boundary value problems for three classes of fully nonlinear elliptic equations. In each case we prove that the solution exists if and only if the underlying domain is the interior of an ellipsoid (or ellipse in two dimensions). The proofs make