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Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries

✍ Scribed by Cristian Enache; Shigeru Sakaguchi

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
117 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 use of the uniqueness theorem, maximum principles or some geometric arguments involving the curvatures of the free boundary. Β© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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