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arXiv · 1305.2312

Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp\`ere type

Barbara Brandolini·Nunzia Gavitone·Carlo Nitsch·Cristina Trombetti
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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.

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Barbara Brandolini, Nunzia Gavitone, Carlo Nitsch, Cristina Trombetti. 2013-05-10. Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp\`ere type. https://arxiv.org/abs/1305.2312

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