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.

Brandolini B., Gavitone N., Nitsch C., & Trombetti C. (2014). Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 101(6), 828-841 [10.1016/j.matpur.2013.10.005].

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

Brandolini B.;
2014

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.
Settore MAT/05 - Analisi Matematica
Brandolini B., Gavitone N., Nitsch C., & Trombetti C. (2014). Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 101(6), 828-841 [10.1016/j.matpur.2013.10.005].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/494159
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