A mean-value inequality for non-negative solutions to the linearized Monge-Ampere equation

FORZANI, L. Y MALDONADO, D.

Potential Analysis

Año: 2009 vol. 30 p. 251 - 270

We prove a mean value inequality for non-negative solutions to Lϕu = 0 in any domain  ⊂ Rn, where Lϕ is theMonge–Ampère operator linearized at a convex function ϕ, under minimal assumptions on the Monge–Ampère measure of ϕ. An application to the Harnack inequality for affine maximal hypersurfaces is included.