Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type
- Authors: Brandolini B.; Gavitone N.; Nitsch C.; Trombetti C.
- Publication year: 2014
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/494159
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.