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Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries
Author(s) -
Enache Cristian,
Sakaguchi Shigeru
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810170
Subject(s) - overdetermined system , mathematics , ellipsoid , uniqueness , free boundary problem , ellipse , boundary value problem , elliptic boundary value problem , domain (mathematical analysis) , nonlinear system , mathematical analysis , mathematical proof , boundary (topology) , elliptic curve , geometry , physics , quantum mechanics , astronomy
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. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim