Interior gradient estimates for solutions to the linearized Monge-Ampere equation

Let phi be a convex function on a convex domain Omega subset of R-n, n >= 1. The corresponding linearized Monge-Ampere equation is trace(Phi D(2)u) = f, where Phi := det D-2 phi(D-2 phi)(-1) is the matrix of cofactors of D-2 phi. We establish interior Holder estimates for derivatives of solutions to such equation when the function f on the right-hand side belongs to L-p(Omega) for some p > n. The function phi is assumed to be such that phi is an element of C((Omega) over bar) with phi = 0 on partial derivative Omega and the Monge-Ampere measure det D-2 phi is given by a density g is an element of C(Omega) which is bounded away from zero and infinity. (C) 2011 Elsevier Inc. All rights reserved.