A mean-value inequality for non-negative solutions to the linearized monge-ampère equation

Abstract

We prove a mean value inequality for non-negative solutions to L in any domain Ω∈∈ n , where L is the Monge-Ampère operator linearized at a convex function, under minimal assumptions on the Monge-Ampère measure of. An application to the Harnack inequality for affine maximal hypersurfaces is included. © 2009 Springer Science+Business Media B.V.