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

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

Research output: Contribution to journalArticlepeer-review

3 Citations (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.
Original languageEnglish
Pages (from-to)828-841
Number of pages14
JournalJOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES
Volume101
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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