Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

Barbara Brandolini; Barbara Brandolini; Carlo Nitsch; null Gavitone; Cristina Trombetti

Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

Barbara Brandolini, Barbara Brandolini, Carlo Nitsch, Gavitone, Cristina Trombetti

Matematica e Informatica

Risultato della ricerca: Article › peer review

3 Citazioni (Scopus)

Abstract

The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.

Lingua originale	English
pagine (da-a)	828-841
Numero di pagine	14
Rivista	JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES
Volume	101
Stato di pubblicazione	Published - 2014

All Science Journal Classification (ASJC) codes

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title = "Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp{\`e}re type",

abstract = "The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.",

author = "Barbara Brandolini and Barbara Brandolini and Carlo Nitsch and Gavitone and Cristina Trombetti",

year = "2014",

language = "English",

volume = "101",

pages = "828--841",

journal = "Journal des Mathematiques Pures et Appliquees",

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T1 - Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

AU - Brandolini, Barbara

AU - Nitsch, Carlo

AU - Gavitone, null

AU - Trombetti, Cristina

PY - 2014

Y1 - 2014

N2 - The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.

AB - The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.

UR - http://hdl.handle.net/10447/494159

M3 - Article

VL - 101

SP - 828

EP - 841

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

SN - 0021-7824

ER -

Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

Abstract

All Science Journal Classification (ASJC) codes

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