Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries

Cristian Enache; Shigeru Sakaguchi

doi:10.1002/mana.200810170

Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries

Cristian Enache, Shigeru Sakaguchi

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1872-1879
Number of pages	8
Journal	Mathematische Nachrichten
Volume	284
Issue number	14-15
DOIs	https://doi.org/10.1002/mana.200810170
Publication status	Published - 2011 Oct 1
Externally published	Yes

Keywords

35B50
35R35
Ellipsoids
Free boundary
Fully nonlinear elliptic equations
MSC (2010) 35J65
Overdetermined problems

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.200810170

Cite this

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AU - Sakaguchi, Shigeru

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AB - 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.

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KW - 35R35

KW - Ellipsoids

KW - Free boundary

KW - Fully nonlinear elliptic equations

KW - MSC (2010) 35J65

KW - Overdetermined problems

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JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

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ER -

Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries

Abstract

Keywords

ASJC Scopus subject areas

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