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 |
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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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- ???subjectarea.asjc.2600.2604???