Global \(W^{2,p}\) estimates for solutions to the linearized Monge-Ampère equations (Q2448325)

This paper is concerned with the linearized Monge-Ampère equations, and there are established global \(W^{2,p}\) estimates of their solutions. The study is developed in bounded convex domains of the Euclidean space, and the main tools are the Caffarelli-Gutierrez interior Harnack estimates and the Savin localization theorem. There are also obtained density estimates, which improve the standard power decay estimates. The proof of the main result combines related density estimates, a covering theorem, and a strong-type \(p-p\) estimate for the maximal function.