Pith. sign in

REVIEW

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1305.2312 v2 pith:35LPMBPR submitted 2013-05-10 math.AP

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

Barbara Brandolini , Nunzia Gavitone , Carlo Nitsch , Cristina Trombetti This is my paper
classification math.AP
keywords boundaryoverdeterminedproblemvalueaffineappliedauxiliarycharacterization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original 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.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.