Interior gradient estimates for solutions to the linearized Monge–Ampère equation

Let ? be a convex function on a convex domain Ω⊂Rn, n?1. The corresponding linearized Monge–Ampère equation istrace(ΦD²u)=f, where is the matrix of cofactors of D²?. We establish interior Hölder estimates for derivatives of solutions to such equation when the function f on the right-hand side belongs to Lp(Ω) for some p>n. The function ? is assumed to be such that with ?=0 on ∂Ω and the Monge–Ampère measure is given by a density g∈C(Ω) which is bounded away from zero and infinity.