Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp\`ere type
Analysis of PDEs
2013-10-14 v2
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.
Keywords
Cite
@article{arxiv.1305.2312,
title = {Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp\`ere type},
author = {Barbara Brandolini and Nunzia Gavitone and Carlo Nitsch and Cristina Trombetti},
journal= {arXiv preprint arXiv:1305.2312},
year = {2013}
}
Comments
Title change. Few typos