6533b7dcfe1ef96bd1271f70

RESEARCH PRODUCT

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

Nunzia GavitoneBarbara BrandoliniCarlo NitschCristina Trombetti

subject

Curvature flowApplied MathematicsGeneral MathematicsMathematical analysisFully nonlinear equationsAuxiliary functionEllipsoidSobolev inequalityOverdetermined systemMaximum principlesMaximum principleSettore MAT/05 - Analisi MatematicaAffine curvatureOverdetermined problemsEntropy (information theory)Boundary value problemMathematics

description

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.

yearjournalcountryeditionlanguage
2014-06-01
10.1016/j.matpur.2013.10.005http://hdl.handle.net/11588/567195